Quantum mechanics Definition and 994 Threads

  1. Peter Morgan

    I Against Collapse: A Mathematical Argument

    One sees "Collapse" language all the time, and yet it seems there's a very simple argument that shows that it's not necessary. Suppose we measure ##\hat A## twice, at an earlier and at a later time, then the joint probability density for the measurement results being ##u## and ##v##...
  2. astrocytosis

    Volume integral over a gradient (quantum mechanics)

    Homework Statement 1) Calculate the density of states for a free particle in a three dimensional box of linear size L. 2) Show that ##\int f \nabla g \, d^3 x=-\int g \nabla f \, d^3 x## provided that ##lim_{r \rightarrow \inf} [f(x)g(x)]=0## 3) Calculate the integral ##\int...
  3. L

    I Symmetries in quantum mechanics and the change of operators

    When we make a symmetrie transformation in a quantum system, the state ##|\psi \rangle## change to ## |\psi' \rangle = U|\psi \rangle##, where ##U## is a unitary or antiunitary operator, and the operator ##A## change to ##A'##. If we require that the expections values of operators don't change...
  4. 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.
  5. Demirci Kawa

    B Does the brain use quantum mechanics?

    We need quantum physics for cognitive neuroscience ?
  6. 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...
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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...
  14. 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.
  15. 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...
  16. 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...
  17. 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.
  18. 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
  19. 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...
  20. Demystifier

    Against "interpretation" - Comments

    Greg Bernhardt submitted a new blog post Against "interpretation" Continue reading the Original Blog Post.
  21. 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...
  22. 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...
  23. 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##...
  24. Konte

    I Resolvent formalism in quantum mechanics

    Hi everybody, While reading some quantum mechanics book, I met the resolvent formalism which is presented as more powerful than the pertubative approach. For a system with a hamiltonian ## H = H_0 + H_{int} ##, when the interaction part ## H_{int} ## is no more a pertubation but rather having...
  25. I

    I Particle in a box, boundary co-ordinate change

    If you have a particle in a 1-d box with a finite potential when ##0 < x < L ## and an infinite potential outside this region, then the normalised wavefunction used to describe said particle is ## \psi (x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L})##. However, if you had say instead a finite...
  26. Bilal Rajab Abbasi

    I Introduction to Quantum Mechanics

    Hi! I am Bilal Rajab. I have a question regarding Quantum Physics. From where can we learn about Quantum Physics and what is its relation to Classical Physics? Why is there not one single Physics...? Thanks Regards, Bilal Rajab Abbasi
  27. S

    I Griffiths' Intro to Quantum Mechanics - primed variables

    Hello,I have been going through Griffiths’ Intro To Quantum Mechanics in an attempt to self-teach myself some quantum mechanics. I am currently in section 3.4 (Generalized Statistical Interpretation) I am seeing a “step” occur more than once. When I first came across it, while I didn’t...
  28. W

    I Is quantum mechanics formulated from 1st principles?

    I was surprised recently to learn that one of the reasons both Newton and Einstein were so revolutionary was that they performed a neat mathematical trick. For Newton, it was the mathematical derivation of Kepler's laws from Newton's laws of gravitation and motion. For Einstein, it was the...
  29. J

    I Retro-causality thought experiment

    It has been mostly substantiated by virtue of experiments such as wheelers delayed choice quantum eraser experiment that we are able to retroactively impact past events of particles. However could this apply to the universe. When physicists are carrying out experiments today, which are creating...
  30. C

    De Broglie wavelength of an electron

    I'm reposting this thread with some editing suggested by fresh_42: 1. Homework Statement Calculate the mass, velocity and the de Broglie wavelength of an electron and an alpha particle, given the kinetic energy K = 2MeV Homework EquationsThe Attempt at a Solution please find attached![/B]...
  31. ParticleMan

    I Open Source Quantum Mechanics Visualization Software

    Are there any folks here who use open source alternatives to Matlab and Mathmatica for visualization of quantum mechanics? Also, are you aware of any introductory quantum material for that tool? If not, do you think such a thing would be worthwhile for visual leaners? Why or why not? I have...
  32. R

    Quantum Self education in modern physics

    In my physics education, I shied away from heavily theoretical stuff like General Relativity. I took the required sequence in Quantum Mechanics but having never used it on the job, much of that knowledge has faded too. I started a course in Quantum Field Theory but dropped it. I had friends...
  33. R

    A Causal Nonseparability: Quantum Mechanics & Causal Principles

    Are timelike entanglement and experiments demonstrating causal non-separability by quantum superposition of causal orders an indication that causal principles may not be applicable to quantum mechanics?
  34. MatthijsRog

    I Role of determinate states in quantum mechanics

    Hi, I'm an undergrad, following my very first serious course in QM. We're following Griffith's book, and so far we're staying close to the text in terms of course structure. Griffiths starts out his book by postulating that each and every state for any system \Psi must be a solution to the...
  35. RUTA

    Insights The Quantum Mystery of Wigner's Friend - Comments

    Greg Bernhardt submitted a new blog post Wigner's Friend Continue reading the Original Blog Post.
  36. Mathfan7

    B How to determine the wavefunction of photons?

    Hi, I'm sorry if this question has already been answered somewhere and I'm just too incompetent to find it, buuut: As the title already says, I really do not get that part of quantum physics (if you can even say I'm getting ANY part at all...). As I searched all Google for an answer I just...
  37. S

    A Could information in a boundary be modified once encoded?

    Could information in a boundary be modified once encoded in holographic principle?There are models of universes where holographic principle has a different correspondence (there is absolutely no reason to assume that this would hold true for all possible universes. You could have a universe...
  38. Another

    I Question about Operators in Quantum Mechanics

    I study on quantum mechanics and I have question about operator. In one dimension. How do we know ## \hat{x} = x## and ## \hat{p}_{x} = -i \bar{h} \frac{d}{dx} ## When schrodinger was creating an equation, which later called "the schrodinger equation". How does he know momentum operator equal...
  39. J

    A Hardy's Paradox and lorentz invariant realist interpretation

    Does Hardy's paradox show that all realist interpretations cannot be made lorentz invariant? Or is it just realist hidden variable theories?
  40. W

    Canonical Quantization: Steps to Find iħ

    Homework Statement For the canonically quantized operators, what are the step in between? how do you get the answer iħ? [q^,p^]=iħ q^ is the coordinate and p^ is the momentum.
  41. V

    Hamiltonian for a 1D-spin chain

    Homework Statement [/B] A 1D spin chain corresponds to the following figure: Suppose there are ##L## particles on the spin chain and that the ##i##th particle has spin corresponding to ##S=\frac{1}{2}(\sigma_i^x,\sigma_i^y,\sigma_i^z)##, where the ##\sigma##'s correspond to the Pauli spin...
  42. RUTA

    Insights The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations - Comments

    Greg Bernhardt submitted a new blog post The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations Continue reading the Original Blog Post.
  43. beefbrisket

    I Computing inner products of spherical harmonics

    In this video, at around 37:10 he is explaining the orthogonality of spherical harmonics. I don't understand his explanation of the \sin \theta in the integrand when taking the inner product. As I interpret this integral, we are integrating these two spherical harmonics over the surface of a...
  44. Alex Petrosyan

    Studying Are there any good exercise books for Quantum Mechanics?

    hi, I’ve been walking through posts on this forum, and found plenty of book recommendations for QM. My problem is, I haven’t had enough practice in a long while. I could go over Solved Problems in e.g. Galitsky, or Gasiorowitz, but they seem to be a little far from what I want to test...
  45. J

    I Causality and quantum physics

    Let me present what I think is the understanding of a particular situation in quantum mechanics, and ask people to tell me whether I am right or wrong. To say that everything happens randomly in QM would be misleading at best. We get at least statistical prediction. But discussions such as the...
  46. P

    I Momentum of a stationary particle/wave?

    We are all familiar with Heisenbergs uncertainty principle. When we determine the position of a particle or wave, the uncertainty of momentum reach infinity. So let's say I have a machine that measures the position very very precisely. Then the uncertainty of this non-moving particles momentum...
  47. Rabindranath

    Angular momentum operator for 2-D harmonic oscillator

    1. The problem statement I want to write the angular momentum operator ##L## for a 2-dimensional harmonic oscillator, in terms of its ladder operators, ##a_x##, ##a_y##, ##a_x^\dagger## & ##a_y^\dagger##, and then prove that this commutes with its Hamiltonian. The Attempt at a Solution I get...
  48. thariya

    A Independence of Operator expectation values

    Hi! I want to know under what conditions the operator expectation values of a product of operators can be expressed as a product of their individual expectation values. Specifically, under what conditions does the following relation hold for quantum operators (For my specific purpose, these are...
  49. P

    Finding the quantized energies of a particle

    Homework Statement Okay, so the question I'm trying to solve is to find the quantized energies for a particle in the potential: $$V(x)=V_0 \left ( \frac{b}{x}-\frac{x}{b} \right )^2$$ for some constant b. The Attempt at a Solution I am following along with the derivation of the quantized...
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