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##...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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.
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
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...
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...
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...
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...
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...
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
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...
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...
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...
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]...
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...
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...
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?
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...
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...
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...
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...
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.
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...
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...
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...
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...
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...
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...
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...
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...