Quantum mechanics Definition and 995 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. H

    I Does wave function get updated instantly as environment changes?

    Suppose we have in a box a particle that is travelling left and right at some speed, bouncing off the walls of the box. The wall on the right is then removed such that the particle would be free to escape the box. Does the wave function of the particle get "updated" instantly the moment the...
  2. Dr_Nate

    I Why do ##t## and ##-i\hbar\partial_t## not satisfy the definition of a linear map/operator in Hilbert space?

    It is common to say that ##t## and ##-i\hbar\partial_t## are not operators in quantum mechanics. But I haven't seen a satisfying justification. As an example of the precision of our discourse, someone has said that ##-i\hbar\partial_t## satisfies the definition of Hermicity, but it is not an...
  3. LightPhoton

    I Volume of momentum space of an ideal gas

    In *An Introduction to Thermal Physics* by Schroeder, while deriving the multiplicity of an ideal gas makes the following statements (image below): Even in quantum mechanics, the number of allowed wavefunctions is infinite. But the number of independent wavefunctions (in a technical sense...
  4. robotkid786

    Courses Open University (ENG/UK)

    Hi. I'm studying a degree in maths/physics with the open university through the "combined STEM" degree programme. I wanted to know, do i require quantum mechanics modules if I wanted to focus on cosmology in the future? My current module options are: Mathematical Methods and Fluid Mechanics...
  5. damarkk

    Anharmonic Quantum Oscillator

    I have one tremendous doubt about it. On ##t=0## the state of the oscillator is ##| \Psi (t) \rangle = | 1 \rangle ##. The perturbation is ##V(x)=\alpha x^3 = \alpha (\frac{\hbar}{2m\omega})^{3/2} (a+a^{\dagger})^3 = \gamma (a^3+3Na+3Na^{\dagger} + 3a + (a^{\dagger})^3)##. The only possible...
  6. damarkk

    Hydrogen Atom in an electric field along ##z##

    There is an hydrogen atom on a electric field along ##z## ##E_z= E_{0z}## . Consider only the states for ##n=2##. Solving the Saecular matrix for find the correction to first order for the energy and the correction to zero order for the states, we have: ##| \Psi_{211} \rangle##, ##|...
  7. wirefree

    I My problem with time-dependent Schrodinger equation

    Section 3.3 titled 'Solutions of the time-dependent Schrödinger equation' states in its 1st line that the time-dependent solution is not an eigenvalue equation: The same section ends with a comment on eigenstates: How do you reconcile this: are solutions to the time-dependent equation...
  8. S

    I Will all objects in the Universe transform into black holes through quantum tunneling?

    If I understood it correctly, at enormous timescales into the future, it is theoretically expected that eventually stable massive structures (like white/black dwarfs) will suffer quantum tunneling events that would make small pieces of them slowly turn into black holes that would rapidly decay...
  9. H

    I Why is m_j not a good quantum number in strong-field Zeeman effect?

    This textbook claims ##m_j## is not a "good" quantum number because the total angular momentum (of an electron of a hydrogen atom placed in a strong uniform magnetic field) is not conserved. I don't understand why ##m_j## is not a "good" quantum number. Since ##J=L+S##, ##J_z=L_z+S_z##. Since...
  10. Q

    I Poisson spot with single photons

    I suppose that when carried out a Poisson spot with photons one at a time should have to be observed. I tried to find such experiment but i got 0 result. it seems that nobody cared about that. But i think such experiment would be very important as it will show that the wavefunction can have...
  11. H

    I Valid to use <1/r3> to get spin-orbit correction to H? (perturbation)

    Below is the derivation of E1so, the first-order correction to the Hamiltonian due to spin-orbit coupling of the election in hydrogen atom. My question is whether it's valid to use [6.64] (see below). ##<\frac{1}{r^3}>## I believe is ##<\psi_{nlm}|\frac{1}{r^3}|\psi_{nlm}>##, but ##\psi_{nlm}##...
  12. dasf806

    What Level of Math is Best Before Taking Physics?

    Good day to all. I'm a new member who is fascinated by and interested in physics, quantum mechanics, astronomy, and cosmology, though I never took classes during my schooling. Admittedly, I have basic math skills and worked hard to attain mediocrity in math classes (a living example of the law...
  13. Aurora Program

    Is it possible to transform an electric thunderstorm into an EMP storm?

    TL;DR Summary: Do not get confused with the title, standard thunderstorms are not generally classified as EMP storms because they don't have the power, the scale and nature of the electromagnetic energy involved are greatly different compared to a nuclear EMP detonation, that's exactly the...
  14. S

    B Can energy be stored in a single particle indefinitely?

    Can energy be stored in a single particle without it being lost over time? I mean, photons would be an exampld in principle, but they get redshifted as the universe expands and become less energetic as time goes by We could store that energy in form of kinetic energy for individual...
  15. N

    Electron moving in an electromagnetic field and rotation operator

    Hello, The idea I had was to time evolve the state ##U(\hat{\textbf{b}}, \omega t)| \phi(t) \rangle##, but I'm confused on how to operate with ##H## on such state. I Iwould be glad if anyone could point some way. Thanks!
  16. Golak Bage

    I [QFT-Schwartz Page. 256] Violation of operator exponentiation rule ?

    When computing the projection of time-evoluted state ## |x_j> ## on ## |x_{j+1}> ## it uses the 'completeness' of momentum basis ## \int \frac{dp}{2\pi} |p><p| ##. Next it explicitly states the form of Hamiltonian ## \hat{H} = \frac{\hat{p}^2}{2m}+\hat{V}(\hat{x_j},t_j) ##. Thereafter i believe...
  17. Golak Bage

    A What is the meaning of "Amplitude of Detection" in A. Zee's QFT book?

  18. Tommolo

    A Is the QT "no-cloning theorem" suitable as "Chronological Protection"?

    Just a question: how would the wavefunction "collapse" in a time-reversed universe? Let's take Alice. If she's taking a backward time travel to -say- 2021 and finds herself in 2021, wouldn't that be a (prohibited) quantum cloning of an already measured quantum state? Say, the |Alice 2021⟩ ket is...
  19. Mayhem

    Chemistry Electricity for chemists

    Are there good textbooks which explain electricity in a chemical context better. i.e. for use in measurements (cyclic voltammetry and others), the physics (suitable for a chemist) of electricity in solutions and how solutions can be modelled in circuit diagrams. I have some knowledge of...
  20. S

    I Supressing black hole evaporation?

    A very massive charged black hole could reach a near-extremal state in the right conditions supressing the rate of emission of Hawking radiation (https://physics.stackexchange.com/questions/490524/evaporation-of-large-charged-black-holes) Meanwhile, the radiation emitted by a black hole can be...
  21. LightPhoton

    I How to "derive" momentum operator in position basis using STE?

    I am not able to use Latex for some reason. It is very glitchy and if I do one backspace then it fills my whole screen with multiple copies of the same equation. Thus I am pasting a screenshot of handwritten equations instead. Apologies for any inconvenience. In Introduction to Quantum...
  22. P

    I Is QM generally believed to be able to describe Newtonian mechanics?

    I have a hard time to grok QM. I wonder if it is my fault. Probably QM and all the interpretations are incapable to explain the world as we observe it (either in Newtonian mechanics, or in Special Relativity), not counting gravitation, also not allowing "objective collapse" (which would be a...
  23. gaiussheh

    I Completeness of Eigenfunctions of Hermitian Operators

    I know that completeness (roughly) implies that (almost) all functions can be decomposed into a sum of eigenfunctions of a Hermitian operator. ##\psi=\sum_n \alpha_n \psi_n##. Clearly, there have to be some restrictions on the function itself, and the operator as well. But what is that? My...
  24. D

    Determine unit vector n such that (L dot n)psi(r) = (m*hbar)psi(r)

    First I calculated ##(\vec{n} \cdot L) \psi(r) = -i\hbar(n_{x}(3y-z)+n_{y}(z-3x)+n_{z}(x-y))f(r)## and then tried to solve for ##n_{i}## such that I get (x+y+3z)f(r), and then divide ##n_{i}## by the magnitude of ##\vec{n}## to get the unit vector and m, but when I try doing this, I get the...
  25. elou

    B Disappearance of interference pattern in double slit

    https://www.nature.com/articles/s41598-019-43323-2. Please note Figure 4 p.4 of the article, and the following description: " In Fig. 4(h), the right slit is completely blocked, the interference fringes have disappeared completely and only the diffraction image of the open left slit remains."...
  26. K

    I Conservation of energy after measurement

    so I thought that when a system was measured there could be an interaction between the measurement device or environment and the system but overall energy was conserved, but I came across these 2 articles which seem to imply this is not the case...
  27. K

    Sign Issue with Zitelli Quantum Mechanics 3.6

    I will include a photo. Essentially, we need to prove that dp/dt + the gradient of J(x,t) = 0. We are getting that the two are instead equal and opposite, and have checked with multiple people.
  28. Ibix

    I Constant phase factors in wavefunctions

    I'm trying to repair the dismal state of my knowledge of QM, so I downloaded Tong's notes and have read through them a couple of times and I have a question. Tong says (section 1.1.1, p7 in the pdf) that an overall constant phase factor ##e^{i\alpha}## infront of a wavefunction describes an...
  29. B

    I Many-Worlds and Testable Claims

    Among the most well-known interpretations of Quantum Mechanics is that of the "Many Worlds," in which all possible outcomes of a measured quantum event occur simultaneously in some alternative universe. Now, I realize there is some manner of debate as to whether or not the different...
  30. murshid_islam

    Is "Quantum Mechanics Demystified" a good book for a beginner?

    TL;DR Summary: Is "Quantum Mechanics Demystified" a good book for a beginner for self-studying? I'm a layman with background in high school physics and undergrad calculus. Is "Quantum Mechanics Demystified" by David McMahon a good book for self-studying and learning quantum mechanics?
  31. arivero

    I The lore on complex probabilities

    I think that the lore on the need of having probability interference in quantum mechanics and then a complex probability originates in Feynman interpretation of space-time paths, whose probability is weighed with a complex exponential that approaches a dirac delta. But I can not pinpoint a...
  32. T

    I The theory on the effects of polarizers on particles wavefunctions

    I would like to ask what the current scientific understanding on the abilities of various types of polarizers to affect the wavefunctions of particles is. Its based on an earlier thread OP of mine and one of the replies in the thread. So the Born rule is pretty fundamental to quantum mechanics...
  33. P

    I Is this a valid quantum Cheshire cat?

    I just watched Sabine's Hossenfelder very recent new video on the Quantum Cheshire effect. From experience, everything Sabine's says on either entanglement/quantum interpretations or not-physics, is heavily biased to her worldview. However I thought it was fun to see what she was going to say...
  34. B

    A Can wave particle dualism be replaced by a monistic model?

    In the article “Quantum mechanical measurement in monistic systems theory” doi:10.23756/sp.v11i2.1350 there is no collapse of the wave function and only one world. Can wave particle dualism be replaced by a monistic model?
  35. milkism

    Quantum Mechanics I, finding impuls wavefunction.

    I have this following Gaussian wavefunction. I found the constant C to be $$\sqrt{\sqrt{\frac{2 \alpha}{\pi}}}$$. Now they're asking me to find the normalized impuls wavefunction $$\phi(p)$$. I tried to use the fourier transform relation $$\phi (p) = \int e^{-\frac{i ( p x)}{\hbar}} \Psi...
  36. gentzen

    A Yakir Aharonov's time-symmetric formulation of quantum mechanics

    I recently watched "A New Approach to Quantum Mechanics" by Dr. Yakir Aharonov Part 1 (12.12.2023 | Institute for Quantum Studies) on YouTube (and also Part 2 and 3). I was naive enough to believe it was really new. Only when I searched for a valid reference in order to be allowed to ask about...
  37. M

    Good textbook(s) for self-studying Quantum Physics

    Could you please suggest a good textbook for self-studying quantum mechanics? Not something too advanced. I have a math degree, so I'm not averse to equations.
  38. H

    A Is there still a Wigner's friend paradox?

    Happy new year to all the forumers. The Wigner's friend paradox appeared in the early years of quantum mechanics: Wigner knows that his friend looked inside the box to see if the cat is dead or alive. He has two cells in his mind to put what his friend saw. As he ignores the result, he may...
  39. S

    What are the latest developments in discrete Quantum Field Theories?

    I have been interested in physics for a very long time. Initially in high school celestial mechanics and soon afterwards quantum mechanics. During my chemistry studies I specialized in quantum chemistry at the end of my bachelor and continued to do a Bachelor and Master in pure Mathematics, with...
  40. milkism

    Finding <x> using raising and lowering operators and orthonormality

    I have this 1D LHO problem. https://gyazo.com/4cd913d9da3a743443ef7dc2d1c2ab1e For ##\psi_n (x)## I get $$\left( \frac{\alpha}{\sqrt{\pi} 2^n n!} \right) ^{\frac{1}{2}} e^{\frac{- \alpha^2 x^2}{2}} H_n(x)$$ with ##E_n = (n+ \frac{1}{2}) \hat{h} \omega##. where ##\hat{h}## is hbar. For...
  41. J

    B Question about double-slit experiment

    s
  42. Spathi

    I Mathematical basics of quantum mechanics

    I study QM, in particular I need to implemend the computation of vibrational spectrum for polyatomic molecules by forca constants in the "rigid rotor - harmonic oscillator" approximation in my program Chemcraft. I have watched some videos from the channel "Professor Dave explains". The...
  43. J

    Quantum Quantum mechanics textbook for 2nd year student

    I desperately need a good resource for quantum mechanics. This semester, our lectures have been absolutely terrible. Though I managed to avoid this by studying hard, the lectures and notes were so critically inadequate that most students (not including me) used ChatGPT to complete any online...
  44. Kyuubi

    Semi-infinite + finite potential well QM

    I want to verify some inspection I'm making at this problem. Because of the infinite barrier at ##x=0##, we expect the wave function to take the value 0 there to preserve continuity. As such, we can make the conclusion that the wave function will just be a sine term in the [0,a] region. But...
  45. M

    A Derivation of Generalized Khon-Sham Scheme

    Hello, I am following the paper: https://www.yumpu.com/en/document/read/42212557/exact-exchange-in-density-functional-calculations and I am confused on page 14 where the generalized Kohn-Sham equations are derived. I follow that the ground state energy is The minimization of this step leads...
  46. D

    I Measurements and uncertainty principle

    Dear friends please help me, for I am completely confused and can not understand the logical connection between two postulates of quantum mechanics. One postulate states, that if some observable is being measured, for instance coordinate, then the superposition of many possible states, which...
  47. Lynch101

    I Looking For Help Understanding Bell's Theorem, Hidden Variables & QM

    I was revisiting @DrChinese 's Bell's Theorem with Easy Math which sparked a few questions, which I am hoping might offer a potential path to a deeper understanding of Bell's Theorem and Quantum Mechanics (QM) in general. The explanation uses light polarisation experiments to explain how we...
  48. J

    Quantum Mechanics homework question on wavefunctions

    Absolutely no clue on how to even begin this question due to the exceptionally poor quality of our lectures, who has also flatly refused to give out any solutions, which I could have used to understand what is going on. I assume the energy has to be obtained by using the eigenfunction equation...
  49. fisicaltibs

    How do long fingernails affect daily activities and overall health?

    I hold a PhD in physics and am very interested in education. I have been a high school math teacher, teaching assistant (both graduate and undergraduate, physics and chemistry), and tutor.
  50. 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".
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