All Questions
Tagged with homework-and-exercisesquantum-mechanics
2,774 questions
7votes
2answers
540views
Schrodinger equation has NO solution for infinite-finite potential well?
Consider the following potential $$V(x)= \begin{cases} +\infty, &x<x_0 \\ 0, & x\in[x_0,L] \\ V_0, &x>L \end{cases}$$ and the associated time-independent Schrodinger equation $$-\...
- 281
0votes
0answers
44views
Request for help deriving wave function for Hydrogen (FLP Vol. III Eq. 19.30) [closed]
Basically, I've been going slightly mad for three days trying to derive one of the equations from the Feynman's course, namely eq. 19.30 from Vol.3, or the spherically symm. wave function for H at the ...
- 1
1vote
1answer
46views
Decay of spin-3/2 particle to either two spin-1/2 or two spin-0 particles
This question may be quite naive, so I apologize in advance. Thing is, I'm working through an exercise that asks to evaluate the allowed values of the individual orbital angular momentum after a spin-...
1vote
0answers
45views
Relation between the Von Neumann entropy of a system and of its purification
I am looking at the proof of Lemma 4. (i) of "Information-theoretic treatment of tripartite systems and quantum channels" by Coles et al. (https://doi.org/10.1103/PhysRevA.83.062338) From ...
- 11
1vote
0answers
43views
Existence of bound state in semi-infinite potential [closed]
We consider the bound states of a particle in the following asymmetric finite potential well: $$ V_B(x) = \begin{cases} 0 & (x < a) \quad \text{(Region I)} \\ - V_0 & (a \leq x \leq b) \...
- 405
2votes
1answer
46views
Explicit form of Fock state acting on Weyl operators
In Bratelli and Robinson's $\textit{Operator Algebras and Quantum Statistical Mechanics Vol. 2}$, on page 24, they state that the following is an easy calculation $$\omega_F(W(f)) = \langle \Omega, W(...
0votes
2answers
75views
How many electrons can fit inside a 3D infinite well potential with $n=2$?
So I'm a little confused about the 3D potential well (particle in a box). Its energy is given by the 1D potential well formula with a factor of $(n_x^2, n_y^2, n_z^2)$ at the end: $$ E = \frac{h^2}{...
- 57
1vote
2answers
80views
Griffiths and Schroeter: Transformation of operators
In Example 6.1 of Griffiths and Schroeter,Introduction to Quantum Mechanics (3rd Edition) suggest determining the transformation properties of the operator $\hat{x}$ by the translation operator $\hat{...
- 3,934
1vote
1answer
106views
Question on the square-integrability of the given wavefunction at origin and infinity
I have this function as a wavefunction of a quantum system: $$\psi(r)=N r^a \exp\left(br^2 + cr+\frac d{r^3}+\frac e{r^2}+\frac f{r}\right)$$ where $r$ is the radial parameter ranging on the interval $...
- 13
2votes
0answers
100views
What causes amplitudes to interfere?
I have started working through Quantum Mechanics section of the Exercises for the Feynman Lectures on Physics, but I got stuck on one of the questions. The question is about an idealized version of an ...
-1votes
1answer
64views
Help with the second-quantised form of a one-body operator
This question concerns the steps leading to Eq. 2.11 in Condensed Matter Field Theory by Altland and Simons. Consider a one-body operator $\mathcal{O}_1$ which is diagonal in the basis $\left|λ\right&...
- 544
0votes
1answer
42views
Velocity of de Broglie wave of moving particle with velocity $v$
I came across the following question: To obtain this answer with the frequency term in the relation is doable. But the options given seem to have elimination the term f. The answer given as the ...
1vote
0answers
97views
A 1d Feynman integral: How to compute?
I am trying to evaluate the following integral: $$ I_{n_1,n_2,\alpha} \,=\, \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \, \bigg(\,{ \frac{e^{...
- 604
1vote
0answers
39views
Derive expression for magnetic moment of a 1d magnet
Consider the simplest 1-dimensional magnet given by a chain of 1/2 spins where only neighbors interact. The general form of such magnetic Hamiltonian is given by: $$ \hat H = \Sigma_{i= -\infty}^\...
- 13
1vote
0answers
46views
Newton's equations for the nuclei in the harmonic approximation [closed]
I would like to ask for some help with a derivation I'm trying to understand. Main problem I'm try to solve Exercise 7.4 from Materials Modelling using Density Functional Theory by Feliciano Giustino. ...
- 111
