# What is Quantum mechahnics: Definition and 177 Discussions

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1. ### I In what chapter do Mehra and Rechenberg discuss Pauli matrices?

I am very interested in how Pauli found the Pauli matrices, so I read his original paper, but it didn't give me the perspective I wanted, so I went to Mehra and Rechenberg, but here's the thing, after reading Volumes 1, 2 and most of volume 3, I can't find any mention of Pauli matrices anywhere...
2. ### I Normalizing factor of wave function

So on page 256 of Quantum Mechanics - The Theoretical Minimum, it says that the wave function of a momentum eigenvector, with respect to the position eigenbasis is ##\psi_p(x)=Ae^{\frac{ipx}{\hbar}}##, and ##A## must be ##\frac{1}{\sqrt{2\pi}}## to keep it a unit vector. However why must...
3. ### Sequences of measurements in quantum mechanics

ATTEMPT AT SOLUTION: I understand if looking for positive this will be +hwo/2 (hbar) for Sz so must find |a|^2. and if looking for negative this will be -hwo/2 (hbar) so must find |b|^2. If asked to find say Sx and original question in Sz, we must find new eigenstates associated with this state...

29. ### Perturbation from a quantum harmonic oscillator potential

For the off-diagonal term, it is obvious that (p^2+q^2) returns 0 in the integration (##<m|p^2+q^2|n> = E<m|n> = 0##). However, (pq+qp) seems to give a complicated expression because of the complicated wavefunctions of a quantum harmonic oscillator. I wonder whether there is a good method to...
30. ### Spin probability of a particle state

Starting with finding the probability of getting one of the states will make finding the other trivial, as the sum of their probabilities would be 1. Some confusion came because I never represented the states ##|\pm \textbf{z}\rangle## as a superposition of other states, but I guess you would...
31. ### I Is this something like a Wick rotation?

Please look at this YDSE with two orthogonal polarizers...
32. ### I Properties of a unitary matrix

So let's say that we have som unitary matrix, ##S##. Let that unitary matrix be the scattering matrix in quantum mechanics or the "S-matrix". Now we all know that it can be defined in the following way: $$\psi(x) = Ae^{ipx} + Be^{-ipx}, x<<0$$ and $$\psi(x) = Ce^{ipx} + De^{-ipx}$$. Now, A and...
33. ### Studying Does anyone know where to find solutions to MIT's 8.04 psets?

Specifically, for this section/year: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/assignments/. I ask for those problem sets because I am following Prof. Barton Zwiebach's lectures on edX and the website doesn't seem to parse the HTML for the assignments always. What...
34. ### Quantum motion of a charged particle in a magnetic field

Once I know the Hamiltonian, I know to take the determinant ##\left| \vec H-\lambda \vec I \right| = 0 ## and solve for ##\lambda## which are the eigenvalues/eigenenergies. My problem is, I'm unsure how to formulate the Hamiltonian. Is my potential ##U(r)## my scalar field ##\phi##? I've seen...
35. ### (QM) Number of states with Energy less than E

Hi, so I'm having trouble with a homework problem where it asks me to find the number of states with an energy less than some given E. From this, I was able to work out the energy E to be $$E = \frac{\hbar^2}{2m} \frac{\pi^2}{a^2} \left( n_x^2 + n_y^2 + n_z^2 \right)$$ and...
36. ### I Quantum Mechanics Particle in a Box

I need help .I did not A) E < V0 for T =? (passing coefficient ) B) E = V0 for T = ? C ) E > V0 for T =? A
37. ### Infinite Square Well with polynomial wave function

Some questions: Why is this even a valid wave function? I thought that a wave function had to approach zero as x goes to +/- infinity in all of space. Unless all of space just means the bounds of the square well. Since we have no complex components. I am guessing that the ##\psi *=\psi##. If...
38. ### I Commutator's Matrix representation

Hello! I have checked commutator matrix form of $$\vec{p}=im/\hbar [H,\vec{x}]$$ but I realized i don't undertand something I have $$[H,\vec{x}]=H\vec{x}-\vec{x}H$$ and $$(H\vec{x})_{i}=H_{ij}x_j$$ & $$\ ( \vec{x}H)_{i}=x_jH_{ji}$$ but what is the second term matrix representation...
39. ### I Questions about QFT and the reality of subatomic particles

I've been reading about Quantum Field Theory and what it says about subatomic particles. I've read that QFT regards particles as excited states of underlying quantum fields. If this is the case, how can particles be regarded as objective? It seems to me that this also removes some of the...
40. ### Find the probability of a particle in the left half of an Infinite Square well

Attempt: I'm sure I know how to do this the long way using the definition of stationary states(##\psi_n(x)=\sqrt{\frac {2} {a}} ~~ sin(\frac {n\pi x} {a})## and ##\int_0^{{a/2}} {\frac {2} {a}}(1/5)\left[~ \left(2sin(\frac {\pi x} {a})+i~ sin(\frac {3\pi x} {a})\right)\left( 2sin(\frac {\pi x}...
41. ### Show that the Hamiltonian is Hermitian for a particle in 1D

I need help with part d of this problem. I believe I completed the rest correctly, but am including them for context (a)Show that the hermitian conjugate of the hermitian conjugate of any operator ##\hat A## is itself, i.e. ##(\hat A^\dagger)^\dagger## (b)Consider an arbitrary operator ##\hat...
42. ### Quantum Alternative Undergraduate Quantum Mechanics book

Hi everyone, was just wondering what people think is a good undergraduate QM book is as opposed to Griffiths. I've read through it, and I have looked and many people say it is good for people who've never been exposed to QM before, but when it comes to solving problems I struggle a lot, and...
43. ### Expectation value of angular momentum

⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩
44. ### I Confused about some notation used by Griffiths

I worked out the expectation values of the components of a 1/2 spin particle. However, I'm confused about Griffiths notation for the x and y components. For the x component I got, ## \left< S_x \right> = \frac \hbar 2 (b^*a+a^*b)## which is correct, but Griffiths equates this to ##...
45. ### Infinitesimal Perturbation in a potential well

If I calculate ## <\psi^0|\epsilon|\psi^0>## and ## <\psi^0|-\epsilon|\psi^0>## separately and then add, the correction seems to be 0 since ##\epsilon## is a constant perturbation term. SO how should I approach this? And how the Δ is relevant in this calculation?
46. ### Effects of KE & PE of a Harmonic Oscillator under Re-scaling of coordinates

The wavefunction is Ψ(x,t) ----> Ψ(λx,t) What are the effects on <T> (av Kinetic energy) and V (potential energy) in terms of λ? From ## \frac {h^2}{2m} \frac {\partial^2\psi(x,t)}{\partial x^2} + V(x,t)\psi(x,t)=E\psi(x,t) ## if we replace x by ## \lambda x ## then it becomes ## \frac...
47. ### Is the concept of "wave function collapse" obsolete?

Summary: In the past, physicists talked of the phenomenon of "wave function collapse" very freely, whereas now there seems to be some reservation about it. Why? In reading older popular physics literature, physicists used to talk about "wave function collapse" freely and more often...
48. ### A Random Quantum Walk: Learn & Use w/ Quantum Gates

I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone could simply explain what a random quantum walk is and then explain how they could be useful with...
49. ### I What exactly is the amplitude of an interaction?

I've been reading Griffths' intro to elementary particles and I encountered this symbol that looks similar to "M" called amplitude, which can be calculated by analyzing the Feynman diagram of an interaction. What exactly is it? When I hear amplitude I imagine waves, but not sure what this one's...
50. ### Asymptotic behavior of Airy functions in the WKB method

If it is the asymptotic behavior of the Airy's function what it's used instead of the function itself: Does it mean that the wkb method is only valid for potentials where the regions where ##E<V## and ##E>V## are "wide"?