What is Quantum mechanics: Definition and 995 Discussions

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. R

    I Why Would Observation Change Anything Physically?

    A particle has a 33% chance of being in either position 1, position 2, or position 3. After I observe it, it is in position 1, and not in position 2 or 3. Questions: How do we know it was not already in that position prior to us observing it? Does observation cause position, or is position...
  2. R

    I Communicating Via Quantum Entanglement Using Time Differentiated Pulse

    Which of these premises is impossible or incorrect according to our current understanding of quantum entanglement? Given 2 entangled particles, p1 and p2: Observing paired particle p1 induces a change in spin on paired particle p2. There a way of detecting a change in spin on particle p2...
  3. A. Neumaier

    I Exploring Quantum Gravity's Impact on Quantum Mechanics

    See Peter Shor's comments here and here and Urs Schreiber's comments here.
  4. J

    A Does the effective action make sense in Quantum Mechanics?

    I think the effective action should make sense also in Quantum Mechanics, not only in QFT. But I have never seen described in a QM book as such. Could there be a QM book that uses effective actions? Or maybe in QM effective actions are called another name? I think effective actions in QM could...
  5. A. Neumaier

    I The Philosophy of Quantum Mechanics

    I'd like to point to the book The Philosophy of Quantum Mechanics by C. Friebe et al., Springer 2018. It contains many topics usually underrepresented in foundational discussions of quantum physics, in chapters on many-particle systems and quantum field theory. It also has in its last chapter a...
  6. F

    I Solving the Quantum Mechanics of a Hydrogen Atom

    Hello, I have a little problem understanding the quantum mechanics of a hydrogen atom. Im troubled with the following question: before i measure the state of a (simplified: without fine-, hyperfinestructure) hydrogen atom, which is the right probability density of finding the electron? is it...
  7. A. Neumaier

    A Jürg Fröhlich on the deeper meaning of Quantum Mechanics

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  8. Hawkingo

    I What is the failure of superposition in quantum mechanics?

    In a book it says that "we know of quantum phenomena in the electromagnetic field that represents a failure of superposition,seen from the viewpoint of the classical theory." I want to about what quantum phenomena is he talking about? This was from the page 11 of the book Electricity And...
  9. J

    A What does "solving a quantum mechanics problem" mean?

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  10. A. Neumaier

    Insights The 7 Basic Rules of Quantum Mechanics

    Continue reading...
  11. Benhur

    Larmor precession in a 2D B-field

    I just tried to find the eigenvalues (for the energy), obtaining E = ±(γħ.√(Bo² + Γo²))/2 and the corresponding eigenvectors for the H matrix. But I don't know what to do to create de state vector χ.
  12. W

    Tensor Product of Hamiltonians

    ##U_1 \otimes U_2 = (1- i H_1 \ dt) \otimes (1- i H_2 \ dt)## We can write ## | \phi_i(t) > \ = U_i(t) | \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators. Writing as tensor product we get ## |\phi_1 \phi_2> = (1- i H_1 \ dt) |...
  13. A

    I Which operator for reflection in quantum mechanics?

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  14. J

    I How to derive the energy of a parabolic confining potential in a wire

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  15. L

    I Definition of a symmetry transformations in quantum mechanics

    By the Wigner theorem, symmetries transformations are implemented by operators ##\hat{U}## that are unitary or antiunitary. This is what is written in most books. But I have read somewhere that, to ##\hat{U}## represent a symmetrie, it's necessary that ##\hat{U}^{\dagger} \hat{H} \hat{U} =...
  16. JD_PM

    Nucleon-nucleon scattering; why can we assume ##l=0##?

    I have found the following explanation: Isn't ##l \hbar = mvR## (semi-classical argument) wrong? I'd state ##mvR = \sqrt{l(l+1)} \hbar## instead. Text is coming from Introduction to Nuclear Physics; Krane, pages 87 and 88.
  17. P

    I Lawrence Krauss: Quantum Mechanics is deterministic (video)

    I understand partly what he is saying, but can you discount the measurement effect as a feature of the world? Aren't measurement effects going on all the time between macroscopic and microscopic systems, making it in practice, at times, an indeterministic world? Or is he assuming that...
  18. JD_PM

    Calculating the Fraction of Time Particles Spend Outside a Potential Well

    I want to compute the fraction of time both particles spend outside the finite potential well. All I can get is the probability to find them outside. The wavefunction outside the potential is: $$\frac{d^2\psi}{dr^2} = -L^2 \psi$$ Where: $$L = \sqrt{\frac{2mE}{\hbar^2}}$$ Solving the...
  19. A

    Courses Electromagnetism 1 vs. Quantum Mechanics 2

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  20. LarryC

    Second Quantization - Quasiparticles

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  21. jdou86

    I Confusion about the Concept of Operators

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  22. Haorong Wu

    An electron in an oscillating magnetic field

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  23. A

    Spin-##\frac{1}{2}## particles in infinite square well

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  24. J

    I Relation between spectral radiance and density of cavity

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  25. stevendaryl

    I Wallis' Formula and Quantum Mechanics

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  26. C

    MATLAB_Quantum Well_Finite Difference Method

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  27. Peter Morgan

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  28. astrocytosis

    Volume integral over a gradient (quantum mechanics)

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  29. L

    I Symmetries in quantum mechanics and the change of operators

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  30. A. Neumaier

    Insights A Classical View of the Qubit - Comments

    Greg Bernhardt submitted a new blog post A Classical View of the Qubit Continue reading the Original Blog Post.
  31. Demirci Kawa

    B Does the brain use quantum mechanics?

    We need quantum physics for cognitive neuroscience ?
  32. D

    I Vacuum projection operator and normal ordering

    I've been reading this book, in which the author expresses the vacuum projection operator ##\vert 0\rangle\langle 0\vert## in terms of the number operator ##\hat{N}=\hat{a}^{\dagger}\hat{a}##, where ##\hat{a}^{\dagger}## and ##\hat{a}## are the usual creation and annihilation operators...
  33. H

    I Nuclear spin coupling in molecular (protium) hydrogen

    I'm not sure where this post belongs--here, or nuclear chemistry, quantum mechanics, NMR spectroscopy, etc. Moderator--please feel free to move it to a better location. I'm wondering if a container of liquid hydrogen subjected to a strong magnetic field would have both nuclei of each atom...
  34. astrocytosis

    Darwin term in a hydrogen atom - evaluating expectation values

    Homework Statement Homework Equations VD= -1/(8m2c2) [pi,[pi,Vc(r)]] VC(r) = -Ze2/r Energy shift Δ = <nlm|VD|nlm> The Attempt at a Solution I can't figure out how to evaluate the expectation values that result from the Δ equation. When I do out the commutator, I get p2V-2pVp+Vp2. This...
  35. P

    I Where to publicise some notes on quantum mechanics

    I've struggled to understand quantum mechanics for many years. I've recently written some notes on the subject that address some of the issues that I've found confusing and that I think might be helpful to others. The moderators on Physics Forums, quite reasonably, won't allow me to publicise...
  36. J

    I What is Stochastic Quantum Mechanics (in simple terms)?

    Could someone, in laymen's terms explain to me what stochastic mechanics is?
  37. L

    A Interpretation of state created by the field in free QFT

    Let us consider QFT in Minkowski spacetime. Let ##\phi## be a Klein-Gordon field with mass ##m##. One way to construct the Hilbert space of this theory is to consider ##L^2(\Omega_m^+,d^3\mathbf{p}/p^0)## where ##\Omega_m^+## is the positive mass shell. This comes from the requirement that there...
  38. JD_PM

    A How to explain the nuclear radius of Uranium 238 using QM

    I am studying how to determine the nuclear charge radius from direct measurement of the Coulomb energy differences of nuclei. My book says that there is strong evidence which suggests that the nuclear force does not distinguish between protons and neutrons. Thus changing a proton into a...
  39. Peter Morgan

    A Schrödinger's cat: what's the state?

    A physicist prepares a box and tells us that in the box there is a cat that is in a superposition of being alive and being dead. How can we be sure whether they're telling the truth? Is the state a superposition or a mixture? If we open the box and measure only whether the cat is alive, using...
  40. Yourong Zang

    Eigensolution of the wave function in a potential field.

    1. Homework Statement Consider a potential field $$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$ The eigenfunction of the wave function in this field suffices...
  41. Demystifier

    Insights 9 Reasons Quantum Mechanics is Incomplete - Comments

    Greg Bernhardt submitted a new blog post 9 Reasons Quantum Mechanics is Incomplete Continue reading the Original Blog Post.
  42. learn.steadfast

    I Interpretations of diffusion in Quantum Mechanics.

    Recently, I've been told I was wrong concerning the nature of stationary states and diffusion being related. Even though I pointed out to the people involved that I was merely paraphrasing Max Born, who was apparently quoting the same idea as Linus Pauling. No one has been able to tell me...
  43. A. Neumaier

    A Initial-value problem for Bohmian mechanics

    Does Bohmian mechanics have a mathematically well-defined initial-value problem with unique solution for given initial data? The right hand side of the guiding equation has singularities at all configuration space positions where ##\psi## vanishes. Thus the particle dynamics breaks down. Thus...
  44. K

    Quantum The main source books for quantum mechanics?

    I would like to know which books are the main sources for the Quantum mechanics 1/2 courses, and the professors use them most during their courses? Thanks for you reply in advance.
  45. D

    Quantum Quantum mechanics Zettili 3rd Edition available yet?

    Hi. I really like this book (2nd edition) and was thinking of buying it. I have seen mention of a new edition , the 3rd edition but it seems to be unavailable to buy. Anyone know if the 3rd edition is out yet or soon ? Thanks
  46. D

    Studying John Baez's list of books math prerequisites?

    my current skills in math are differential eq and linear algebra... and I am about to start reading Feynman lectures of physics and planning to read all John Baez's recommended books.. after reading Feynman's, what would be the next best thing to do? learn more math? or jump already to core...
  47. Demystifier

    Against "interpretation" - Comments

    Greg Bernhardt submitted a new blog post Against "interpretation" Continue reading the Original Blog Post.
  48. W

    Quantum Mechanics and Electrodynamics/Electrostatics

    Hi all, I have a question relating to the title above. The uncertainty relation tells us that an electron that is localised (in terms of its PDF) is space has a large uncertainty in momentum space. However in classical electrostatics/dynamics we seem to make attempts to do things like...
  49. Kevin Chieppo

    B Exploring QM: Is Uncertainty a Physical or Measurable Limitation?

    I'm a hobbyist physicist and I just started studying QM through watching Leonard Susskind's lectures on the Stanford Youtube channel. I get the idea of it being impossible to precisely know both a subatomic particle's position and momentum, but is this actually a physical limitation? Or is it...
  50. Another

    Question commutation in quantum mechanics

    Homework Statement Show that ##[L_{x}^2,L_{y}^2]=[L_{y}^2,L_{z}^2]=[L_{z}^2,L_{x}^2]## Homework Equations ##L^2 = L_{x}^2+L_{y}^2+L_{z}^2## ##L_x = yp_z-zp_y## ##L_y = zp_x-xp_z## ##L_z = xp_y-yp_x## ##[x_i,p_j]=iħδ_{ij}## ##[L_x,L_y]=iħL_z## ##[L_y,L_z]=iħL_x## ##[L_z,L_x]=iħL_y##...
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