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. Ashish Somwanshi

    Measurement problem quantum mechanics

    Is the answer 0.748?
  2. Q

    Quantum Advanced Quantum Mechanics Textbooks: Derivations of Equations

    Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the schrodinger equation fully and step by step.
  3. I

    Quantum Mechanics problem: Determine the value of the constant

    I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.
  4. Ashish Somwanshi

    Measurement problem quantum mechanics

    I was not able to attempt since I don't know which formula or method can be used to solve the problem
  5. S

    More Nobel prizes in quantum information?

    Alain Aspect, John Clauser & Anton Zeilinger have rightfully received the Nobel prize for their contributions to quantum information, as they were three of the main pioneers of quantum information. However, is it now impossible or very unlikely that other physicists working on this field (e.g...
  6. B

    Checking assumptions in boundary conditions of double well system

    The idea here (as I'm told) is to use the boundary conditions to get a transcendental equation, and then that transcendental equation can be solved numerically. So I'm making a few assumptions in this problem: 1. The potential ##V(x)## is even, so the wavefunction ##\psi(x)## is either even or...
  7. Graham87

    Condensed Matter Physics - Fermi velocity, etc.

    I have made solutions a-d, but my fermi velocity seems too big.
  8. H

    I Quantum mechanics stationary state

    Hi, I have hard time to really understand what's a stationary state for a wave function. I know in a stationary state all observables are independent of time, but is the energy fix? Is the particle has some momentum? If a wave function oscillates between multiple energies does it means that the...
  9. S

    I Energy from quantum systems in an expanding universe?

    I found a paper (https://arxiv.org/pdf/astro-ph/0411299.pdf) which talks about quantum systems emitting energy due to spacetime expansion. Is this true or only a hypothesis?
  10. sol47739

    I Postive rays in cathode ray tube experiments?

    I read in the following book A history of the sciences by Stephen F. Mason. About the discovery of the electron the write what I attached in the picture. I wonder what do these positive rays traveling in the opposite direction they talk about consist of? Some ions or what? I understand that the...
  11. pokespriter

    I About the position of electrons (uncertainty)

    Hello guys, I don't know if this is the right place to ask, so please be kind :/ I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%. When I asked about the remaining...
  12. sol47739

    I Exploring Electromagnetism & Quantum Mechanics

    In classical electromagnetism I think I have understood the following(please correct me if something is wrong): A charge produces an electric field, a charge moving with constant velocity produces a magnetic field, an accelerating charge emits electromagnetic radiation. In radio antennas this is...
  13. sol47739

    I Polarization of photons quantum mechanically

    What is it of the photon that gets polarized from a quantum mechanical perspective? In the classical perspective it is often thought that it is the oscillating electric field that gets polarized. But in the quantum case: Is it the de Broglie wave function? Or is it the spin and in case it is the...
  14. sol47739

    A Cause of spontaneous emission?

    I am reading this chapter 3 from the book called The Quantum Vacuum by P.Milonni.(Attached in the pdf, look at chapter 3.2 Spontaneous emission)There they say that spontaneous emission is due to both quantum fluctuations and radiation reaction. They say the transitions induced by the quantum...
  15. E

    I Understanding No Energy Degeneracy in Sakurai's Quantum Mechanics

    Hello, I'm hoping someone can help me understand a statement in Sakurai Modern Quantum Mechanics (3rd edition). In particular, in the section that describes free particle in infinite spherical well (page 198, section 3.7.2), after the text has shown that for a given ##l## value, the energy...
  16. Graham87

    Quantum Mechanics - Matrix representations

    I have found J^2 and Jz, but I am not sure how to find Jx and Jy. I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results. Thanks!
  17. R

    On the origin and the evolution of information in the Universe

    [Mentor Note -- thread moved from the schoolwork forums to the technical forums] Homework Statement:: Tentative Note and summary on the origin and the evolution of information in the universe. Relevant Equations:: none As a teacher of physics I got many questions asked by my students when...
  18. Graham87

    Intro to quantum mechanics - Spin and linear algebra

    So this expression is apparently in Sz basis? How can you see that? How would it look in Sy basis for example? The solution is following. They are putting Sz as a basis, bur how do you know that Sz is the basis here? Thanks
  19. Graham87

    Intro to Quantum Mechanics - Formalism normalisation

    I can't figure out how they get i/sqrt(2) for normalisation of c1. Why is it a complex number? If I normalise c1 I just get 1/sqrt(2) because i disappears in the absolute value squared. Thanks
  20. S

    I Many Worlds as Many Histories?

    I was reading this paper from George Smoot (https://arxiv.org/abs/1003.5952) where he assumes the holographic principle as true and conjectures that our universe would be encoded on the "surface" of an apparent horizon as the weighted average of all possible histories. In that way, there would...
  21. G

    I At which point is gravity inconsistent with quantum mechanics?

    I'd like to understand how gravity does not combine with quantum mechanics. At least there is no accepted theory of quantum gravity, so I assume it is not solved? I'm only starting to learn QFT and eventually GR. Maybe, someone can already outline where those theories fail to combine and comment...
  22. Graham87

    Plot the Expectation Value of Spin - Intro to Quantum Mechanics Homework

    I have found an answer to all of them (a-e) but I don’t know how to plot the function. Thanks!
  23. Graham87

    Intro Quantum Mechanics - Dirac notations

    I am learning Dirac notations in intro to quantum mechanics. I don’t understand why the up arrow changes to down arrow inside the equation in c). My own calculation looks like this:
  24. Graham87

    Quantum mechanics - Find S_x and S_y

    I have a lecture slide that shows how to find S_x and S_y. I get all the steps except the last row. Where did 1/2 come from? I think my linear algebra needs polishing. Thanks!
  25. J

    I Black hole singularity vs. quantum mechanics

    I'm wondering about some aspects about black holes (BH) and singularities, but since all my questions have to do mostly with quantum mechanics, I placed this thread in here. OK, let's assume there IS a singularity in the middle of a BH. A) Pauli exclusion principle (PEP) says no two fermions...
  26. D

    I "No objective reality" in quantum mechanics?

    As per title and the TL;DR, I'm curious if there could be some truth in these statements of the headlines I had read recently or are they just sensationalist fluff. Personally, I find these statements very hard to believe. In fact, impossible to believe. But I'm not a QM expert, not even an...
  27. Delta2

    I Earth's orbit not perfect ellipse

    Listen to the following arguments: Earth's orbit isn't perfect ellipse because classically there is the gravitational field of moon and possibly of Mars and Venus which affect it According to general relativity isn't perfect ellipse because there is the curvature of space time which doesn't...
  28. J

    I Dimensions of quantum cell automata's state space

    In the paper C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573 about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...
  29. A. Neumaier

    A Exploring the Limits of Quantum Mechanics: David Wallace's Manuscript (2022)

    David Wallace, The sky is blue, and other reasons quantum mechanics is not underdetermined by evidence, Manuscript (2022). arXiv:2205.00568. From the Abstract: ''I argue that there as yet no empirically successful generalization of'' [Bohmian Mechanics and dynamical-collapse theories like the...
  30. Graham87

    Quantum mechanics - finite square well

    In a) I get that T should be largest where V_0 is least wide, because when V_0 is infinitely wide the particle would be fully reflected. But I don't get how height in b) and energy levels height in c) correlates to T and R. Is it because of their k? I get the opposite answer from the correct...
  31. Graham87

    Quantum mechanics - infinite square well problem

    I have solved c), but don’t know how to solve the integral in d. It looks like an integral to get c_n (photo below), but I still can’t figure out what to make of c) in the integral of d). I also thought maybe you can rewrite c) into an initial wave function (photo below) with A,x,a but don’t...
  32. Salmone

    I Strange Hamiltonian of two particles on the surface of a sphere

    I have a problem with this Hamiltonian: two identical particles of mass ##m## and spin half are constrained to move on the surface of a sphere of radius ##R##. Their Hamiltonian is ##H=\frac{1}{2}mR^2(L_1^2+L_2^2+\frac{1}{2}L_1L_2+\frac{1}{2}S_1S_2)##. By introducing the two operators...
  33. warhammer

    Requesting guidance on Commutators & Intro QM

    I have approached this question step by step as shown in the image attached. I request someone to please guide if I have approached the (incomplete) solution correctly and also guide towards the complete solution, by helping me to rectify any mistakes I may have made. I'm still unsure how to...
  34. Salmone

    I Wavefunction properties tunneling effect

    I am considering tunnel effect with a potential barrier of a certain height that is ##\neq 0## only for ##0 \le x \le a## . I write the Hamiltonian eigenfunctions outside the barrier as:## \psi_E(x)=\begin{cases} e^{ikx}+Ae^{-ikx} \quad \quad x \le0 \\ Ce^{ikx} \quad \quad x\ge a \\...
  35. Salmone

    I Linear combination of states with Pauli's principle

    If I have two identical particles of ##1/2## spin, for Pauli's exclusion principle all physical states must be antysimmetrical under the exchange of the two particles, so ##\hat{\Pi}|\alpha\rangle=-|\alpha\rangle##. Now, let's say for example this state ##\alpha## is an Hamiltonian eigenfunction...
  36. Salmone

    I Separable Hamiltonian for central potential

    In a central potential problem we have for the Hamiltonian the expression: ##H=\frac{p^2}{2m}+V(r)## and we use to solve problems like this noting that the Hamiltonian is separable, by separable I mean that we can express the Hamiltonian as the sum of multiple parts each one commuting with the...
  37. gremory

    A Power series in quantum mechanics

    Just earlier today i was practicing solving some ODEs with the power series method and when i did it to the infinite square well i noticed that my final answer for ##\psi(x)## wouldn't give me the quantised energies. My solution was $$\psi(x) = \sum^{\infty}_{n=0} k^{2n}(\cos(x) + \sin(x))$$...
  38. Lynch101

    B Statistical Independence in Quantum Mechanics

    Very basic question here, about statistical independence in quantum mechanical experiments. The quote from PD below is what prompted the question. When we talk about "some kind of pre-existing correlation" are talking about a simple correlation in the sense of the correlation of sunglasses and...
  39. warhammer

    Cracking Exams: Overcoming Knowledge Gaps for Intro QM

    Summary:: I understand the consensus on PF about studying for knowledge and not merely for "cracking Semester Exams" but I urge you all to go through below thread before attaching to that feeling in my case. Hi. So I have my Exams on Intro QM approaching very soon, which will be a combination...
  40. warhammer

    [Intro QM] Verification requested on possible solution for a question

    Below I have attached an image of my possible solution. I have replaced all the relevant limits. For some reason, I am getting the final value for (i) part as ψ(x)= with an additional √2pi in the denominator. Have I made any errors or is it fine if I take it within the constant A.. In...
  41. Salmone

    I Particle on a cylinder with harmonic oscillator along z-axis

    I need to know if I have solved the following problem well: A spin-less particle of mass m is confined to move on the surface of a cylinder of infinite height with a harmonic potential on the z-axis and Hamiltonian ##H=\frac{p_z^2}{2m}+\frac{L_z^2}{2mR^2}+\frac{1}{2}m\omega^2z^2## and I need to...
  42. P

    A Position basis in Quantum Mechanics

    Can I conceive a countable position basis in Quantum Mechanics? How can I talk about the position basis in the separable Hilbert space?
  43. mohamed_a

    I Classical analogy approach to quantum mechanics

    I have read about several approcahes to bypass some classical restrictions to quantum facts such as the electron being in a torus-like shape to avoid ,the greater than speed of light, rotation paradox . Could you recommend websites , sources or books that give good classical analogy to quantum...
  44. K

    I Particle on a sphere problem in quantum mechanics and its solution

    To solve a particle on a sphere problem in quantum mechanics we get the below equation :##\left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right)-\frac{m^{2}}{\sin ^{2} \theta}\right] \Theta(\theta)=-A \Theta(\theta) ## To solve this differential equation, we...
  45. Mr_Allod

    Position expectation value of 2D harmonic oscillator in magnetic field

    Hello there, for the above problem the wavefunctions can be shown to be: $$\psi_{n,l}=\left[ \frac {b}{2\pi l_b^2} \frac{n!}{2^l(n+l)!}\right]^{\frac12} \exp{(-il\theta - \frac {r^2\sqrt{b}}{4l_b^2})} \left( \frac {r\sqrt{b}}{l_b}\right)^lL_n^l(\frac {r^2b}{4l_b^2})$$ Here ##b = \sqrt{1 +...
  46. P

    Commutation relations between Ladder operators and Spherical Harmonics

    I've tried figuring out commutation relations between ##L_+## and various other operators and ##L^2## could've been A, but ##L_z, L^2## commute. Can someone help me out in figuring how to actually proceed from here?
  47. Salmone

    I Inner products with spherical harmonics in quantum mechanics

    Let ##|l,m\rangle## be a simultaneous eigenstate of operators ##L^2## and ##L_z## and we want to calculate ##\langle l,m|cos(\theta)|l,m'\rangle## where ##\theta## is the angle ##[0,\pi]##. It is true that in general ##\langle l,m|cos(\theta)|l,m'\rangle=0## ##(1)## for the same ##l## even if...
  48. D

    I Ideas about observing position and momentum at the same time

    I am very interested in quantum mechanics/physics and i keep seeing the Heisenberg uncertainty principle and its making me think about other forms of viewing particles. We traditionally use Photons to view something (our eyes), or other forms of radiation/particles, but i know that merely...
  49. thedubdude

    What can a retired electrical engineer learn about physics at 69 years old?

    I join as a 69 year old retired electrical engineer who is interested in physics. I have particular interest in particle physics and quantum mechanics. I don't expect to provide answers on this forum, but I do intend to ask questions.
  50. thedubdude

    B Special Relativity violation via Quantum Mechanics?

    We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...
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