Quantum mechanics Definition and 994 Threads

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Classical physics, the description of physics that existed before the theory of relativity and quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, while quantum mechanics explains the aspects of nature at small (atomic and subatomic) scales, for which classical mechanics is insufficient. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.

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  1. J

    I How Is the Integral from (3-22) to (3-23) Calculated in Quantum Mechanics?

    I don't get the step from (3-22) to (3-23), can you how this integral was calculated? Thanks! Below there is a screenshoot of (3-9). Images are taken from "Intermediate Quantum Mechanics, 3rd Edition - Bethe, Jackiw".
  2. Hak

    I Existential problem on Electromagnetism and the combination of Relativity and Quantum Mechanics

    In Feynman's famous Physics book, in a discussion of the generality of Maxwell's equations in the static case, in which he addresses the problem of whether they are an approximation of a deeper mechanism that follows other equations or not, he says: I was wondering first of all if this was a...
  3. Ugnius

    Can Quantum Mechanics Ket and Bra Methods Solve Scalar Equations?

    Not really even sure how to approach this problem , I would guess if we need scalar answer we would need to combine these two given equations together but I'm unfamiliar with such methods, in the book there is methods to make a ket to a bra and then matrix part transposes and multiplies with the...
  4. C

    How Many People Can Perform Quantum Mechanical Calculations?

    TL;DR Summary: Quantum mechanical calculations are complex and the number of people capable of performing them is limited. In this thread, rough estimates are requested for the number of people that perform quantum mechanical calculations. Please estimate - somehow - the number of people that...
  5. cemtu

    I K-Shell, Low-Energetic Photons & Photoelectric effect

    At low photon energies, the probability of the photoelectric effect to occur increases, but the probability of the photoelectric effect to happen also increases when going towards most inner shells like K shell but inner shells require much more photon energies to be broken, so isn't there a...
  6. cemtu

    I How does a photon interact with the EM field of a nucleus?

    How does a photon interact with EM field of a nucleus thus exchange momentum and recoil the nucleus when pair production happens?
  7. Kinker

    What is Quantum Mechanics? A Beginner's Guide to Understanding the Fundamentals

    I wish you well. I am interested in quantum mechanics.
  8. A

    I What do the authors of the paper mean here exactly by path integral?

    Hi, I am new here so apologies if i am not using the right subforum. I don't have a physics background so i am not very technical but i do have a little bit of understanding. I was reading this paper by hawking/hertog and came across something that ended up confusing me. Here is it: "Pre-big...
  9. E

    Explicit demonstration of a measurement interaction

    $$\newcommand{\bra}[1]{\left \langle #1 \right \rvert} \newcommand{\braxket}[3]{\left \langle #1 \middle \rvert #2 \middle \rvert #3 \right \rangle} \newcommand{\ket}[1]{\left \rvert #1 \right \rangle} \newcommand{\expec}[1]{\langle #1 \rangle}$$ Ballentine asks us the question at the end of...
  10. Islam Hassan

    B Particle Movement in Quantum Mechanics

    Niels Bohr famously said --and I paraphrase-- that QM is an abstract description of nature and that it can only prescribe what we can say about nature rather than what nature is. What does QM say about the movement of a particle? Is this movement positively ascertained to be smooth and...
  11. E

    I On a constructive method of quantum state preparation (Ballentine)

    Ballentine, in his Chapter 8.1, appears to give the attached recipe for *in principle* preparing an (almost) arbitrary (pure) state (of a particle with no internal degrees of freedom) by the method of "waiting for decay to the energy ground state". My questions are fourfold: 1) From (8.1), we...
  12. E

    Ballentine Problem 8.5 (angular momentum)

    I am struggling with the latter, and think that I somehow need to assume ##f## is real-valued to proceed? My work: The position distributions are equal since $$P_{-m}(\mathbf{x}) = |\Psi_{-m}(\mathbf{x})|^2 = |f(r)Y_l^{-m}(\theta,\phi)|^2 = |f(r)(-1)^m(Y_l^{m})^*|^2 =...
  13. Coelum

    I Energy Non-Conservation in Quantum Mechanics

    Dear PFer's, this is a problem I have been struggling with for years. Is energy conserved (not in a statistical sense) in QM? The so-called collapse of the wavefunction, occurring during a measurement process, is incompatible with energy conservation - at least in the general case. A starting...
  14. O

    I What role does Quantum Mechanics play in a internal combustion engine?

    Thermodynamics deal with quantum mechanics all the time, so I wondered what role it played in a internal combustion engine. Could we calculate it and how does it affect the engine's final output?
  15. Stylord

    Particle in a cylindrically symmetric potential (Quantum mechanics)

    Hi, everyone. Please check the following questions (extracted of the cohen Tanpoudji) for the first question, here my Hamiltonian operator. It's easy to see that it commutes with Lz and Pz. Now we can determine a common eigenvector basis for these 3 operators. For the angular part we need to...
  16. ARoyC

    I Tensor Product of Two Hilbert Spaces

    How to prove that the tensor product of two same-dimensional Hilbert spaces is also a Hilbert space? I understand that I need to prove the Cauchy Completeness of the new Hilbert space. I am stuck in the middle.
  17. M

    Seeking books to help me understand the structure of the Hydrogen Atom

    TL;DR Summary: How to learn about the Hydrogen Atom from Level 2 OU Degree I am copleting the second year of the OU physics degree and "understand" what is taught about the Hydrogen atom there, energy levels et al. I am not yet competent in calculus here. I seek a means, buy a book....view...
  18. ARoyC

    I Confusion Regarding a Spectral Decomposition

    Hi. I am not being able to understand how we are getting the following spectral decomposition. It would be great if someone can explain it to me. Thank you in advance.
  19. ARoyC

    I Confusions I have regarding Measurements in Quantum Mechanics

    Hi. This is Annwoy Roy Choudhury. I have just completed my first-year undergraduate studies in Physics. I am new to Quantum Mechanics. There are certain confusions I have regarding Quantum Measurements. It would be really kind of you to help me out. Postulate 3 states, An example is, Let's...
  20. arivero

    I Spontaneous Symmetry Breaking and quantum mechanics

    Confronted with my inability to grasp Witten's Susy QM examples of supersymmetry breaking, I concluded that the problem was that I was not understanding spontaneous symmetry breaking in simpler contexts. It seems that SSB is not possible in QM because of tunneling between the different states...
  21. T

    I How is the Schrodinger equation related to the Heisenberg equation?

    How is the Schrondinger equation related to the Heisenberg equation?
  22. L

    Particle on a ring (components in the postion basis)

    Hi, I have problems with the task part b and g To solve the task, we have received the following information Task b First, I wrote down what the state ##\psi## looks like $$\psi=\frac{1}{\sqrt{N}} \sum\limits_{k}^{} \psi_k$$ $$\psi=\frac{1}{\sqrt{N}} \sum\limits_{k}^{} \frac{1}{\sqrt{N}}...
  23. J

    B Has anyone ever been able to measure Electron size?

    Hello! I was recently listening to StarTalk podcast and (re)learned that the electron is one of the most elusive particles for which there is no known size. Have there ever been any attempts to measure the size of the electron, either directly or indirectly, from either a practical or theory? I...
  24. topsquark

    Algebra Find Algebraic Physics Courses Starting with Classical Mechanics - Dan

    I just finished an online YouTube Quantum Mechanics course by Frederic Schuller. The course was in two parts, the one Schuller was doing was theory; it was an approach I had been trying to develop myself and had never found anywhere. I don't know what exactly to call the course label: it was...
  25. casparov

    Help Solve for the normalization constant of this QM integral

    I'm given the wavefunction and I need to find the normalization constant A. I believe that means to solve the integral The question does give some standard results for the Gaussian function, also multiplied by x to some different powers in the integrand, but I can't seem to get it into...
  26. vibhuav

    I Physical meaning of two independent, non-interacting parts

    I keep coming across this descriptor, "two (or three) independent, non-interacting parts," in many books on QM (for example, Penrose's Shadows of the Mind). It is usually followed by a mathematical description (for example, state vector |A>|B>). I can wrap my mind around the quantum paradox of...
  27. O

    I What do you need to establish that spin is conserved?

    Hi. Question as in the summary. Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum. What do you need to establish that spin is a conserved quantity? I'm finding references to situations where spin is not a...
  28. Demystifier

    I What Defines the Standard and Realist Views in Quantum Mechanics?

    As you may have noticed, I am obsessed with understanding the difference between two views of quantum mechanics, one of which can be called the "standard" view, and the other the "realist" view. The difference, of course, is very complicated, but I believe that the essence and origin of the...
  29. Demystifier

    I Ontology is to quantum theory what hardware is to computation theory

    In interpretations of quantum mechanics there are two types of physicists: those who care about ontology and those who don't. The ontologists, or realists, want to know what is the world made of. The non-realists, on the other hand, think that this question is not relevant to physics. Usually...
  30. P

    I Quantum Mechanics as a Probabilistic forecast of reality

    Is Quantum Mechanics a Probabilistic Forecast of nature?Someone I know told me their interpretation of QM is that QM only a probabilistic forecast of systems like electrons around atoms. I would like someone to analyse this interpretation and say if its valid or not. According to this person we...
  31. lektroon

    I Are Nicolas Gisin's Intuitionist Mathematics Theories Compatible with SR and GR?

    Hello, As a layman in physics, I wonder the ideas of people who have more knowledge in physics than I do about the theories of Swiss Physicist Nicolas Gisin and his arguments about the intuitionist mathematics. Is there a way to reconcile these ideas with more fundamental theories like SR and...
  32. graviton_10

    I Showing that operators follow SU(2) algebra

    For two quantum oscillators, I have raising and lowering operators and , and the number operator . I need to check if operators below follow commutation relations. Now as far as I know, SU(2) algebra commutation relation is [T_1, T_2] = i ε^ijk T_3. So, should I just get T_1 and T_2 in...
  33. L

    B Bell inequality test without polarisation?

    Was trying to understand the inequality test. The only article ever that I've found that explains it simply is the 1981 article, Bringing home the atomic world: Quantum Mysteries For Anybody. All other explanations require trust and understanding of polarisation, which is a huge deal. So i now...
  34. hachi44

    I Principles of Quantum Mechanics - Hans C. Ohanian - 0137127952

    Hi. I looked everywhere for a specific book but I cannot find any pdf copy of it. The book specifics are below: Publication Name: Principles of Quantum Mechanics Author: Hans C. Ohanian Publisher: Benjamin Cummings Publishing Company ISBN-10: 0137127952 ISBN-13L 9780137127955 I would...
  35. HadronPhysics

    A Numerical method to Lippman-Schwinger equation

    There is a question that puzzle me when I apply numerical method to principal value integral. Let me descibe it. We make use of the fact that the integral ##\int_0^\infty \frac{dk}{k^2-k_0^2}## vanishes, namely, $$ \int_0^\infty \frac{dk}{k^2-k_0^2} = 0 . $$ We use this formula to express a...
  36. H

    Why a particle with spin=0 can't posses a magnetic dipole moment?

    Hi, I would like to know why a particle with spin=0 can't posses a magnetic dipole moment? Using Wigner-Eckart theorem for ##\langle j,1,m,0|j,m \rangle## I get ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}## It seems like the right hand side is the magnetic dipole...
  37. H

    Probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##?

    Hi, Given a spin in the state ##|z + \rangle##, i.e., pointing up along the z-axis what are the probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##? My problem is that I'm not sure to understand the statement. It seems like I have to find the probabilities of measuring an eigenvalue...
  38. V

    A How to derive Quantum Mechanics in curved physical space?

    I am following [this YouTube lecture by Schuller][1] where he finds the appropriate formalism for the quantum mechanics in the physical curved space. Everything makes sense to me but at the very end I see that we find the pull backed connection one-form on the base manifold. He says to the end...
  39. O

    I Limit of quantum mechanics as h -> 0

    Starting from the Heisenberg equation of motion, we have $$ih \frac{\partial p}{\partial t} = [p, H]$$ which simplifies to $$ih \frac{\partial p}{\partial t} = -ih\frac{\partial V}{\partial x}$$ but this just results in ## \frac{\partial p}{\partial t} = -ih\frac{\partial V}{\partial x}## and...
  40. K

    B Searching for Quantum Mechanics Lecture on Delayed Choice Experiment

    Hi everybody. Some years ago I came across a video on youtube where they talked about an experiment with small and large envelops, when the small ones were placed into the large ones and then it resulted in something interesting. It might have been an instance of delayed choice, but I am not...
  41. J

    I Why is quantum mechanics not valid for large objects?

    It this correct explanation why quantum is not valid for large object? Why would small object want to hide their information?
  42. C

    A Multiparticle Relativistic Quantum Mechanics in an external potential

    It is often argued that Dirac Equation is not valid as relativistic quantum mechanics requires the creation of antiparticles. But, there are also some arguments that suggest otherwise. For example, I saw Arnold Neumaier's website on this that there are multiparticle relativistic quantum...
  43. CuriousLearner8

    A Eigenvalue Problem of Quantum Mechanics

    Hello, I hope you are doing well. I had a question about the eigenvalue problem of quantum mechanics. In a past class, I remember it was strongly emphasized that the eigenvalues of an eigenvalue problem is what we measure in the laboratory. ##A\psi = a\psi## where A would be the operator...
  44. H

    Unitary vector commuting with Hamiltonian and effect on system

    Hi, I'm not sure to understand what ##| \phi_n \rangle = \sum_i \alpha_i |\psi_n^i## means exactly or how we get it. From the statement, I understand that ##[U,H] = 0## and ##H|\psi_n \rangle = E_n|\psi_n \rangle## Also, a linear combination of all states is also an solution. If U commutes...
  45. yucheng

    I Fermi's golden rule: why delta function instead of density states?

    Sakurai, in ##\S## 5.7.3 Constant Perturbation mentions that the transition rate can be written in both ways: $$w_{i \to [n]} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \rho(E_n)$$ and $$w_{i \to n} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \delta(E_n - E_i)$$ where it must be understood that this expression is...
  46. N

    Average value of components of angular momentum for a wave packet

    I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.
  47. H

    I Spinors and eigenspinors confusion

    Hi, While studying the spin 1/2, I'm facing some confusions about the spinors and the eigenspinors. I understand that ##\chi = \begin{bmatrix}a \\ b \end{bmatrix}## is the spinor with ##\chi_+ = \begin{bmatrix}1 \\ 0 \end{bmatrix}## and ##\chi_-= \begin{bmatrix}0 \\ 1 \end{bmatrix}## the...
  48. Peter Morgan

    I The collapse of a quantum state as a joint probability construction

    The titular paper can be found here, https://doi.org/10.1088/1751-8121/ac6f2f, and on arXiv as https://arxiv.org/abs/2101.10931 (which is paginated differently, but the text and equation and section numbers are the same). Please see the abstract, but in part this 24 page paper argues that we...
  49. Paul Colby

    A Recent papers refuting real-valued quantum mechanics

    So, in a rare instance I actually read APS News, I came across “New Experiment Suggests Imaginary Numbers Must be Part of Real Quantum Physics.” In November 2022, Volume 31, Number 10. Since complex numbers are isomorphic to a real 2x2 matrix algebra, I was confused how such a claim can be...
  50. H

    Allowed energy for a potential in quantum mechanics

    Hi, I'm working on a problem where I need to find the different energies allowed for a potential, and I found this link https://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html, which is similar of what I'm doing. I'm using mathematica to find the values of E. However, I'm not sure how...
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