All Questions
Tagged with wavefunction homework-and-exercises
549
questions
5
votes
2
answers
493
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Physical meaning of each term of the square modulus of a wave function
The expression below is the square modulus of the wave function of a harmonic potential ($V=\frac{1}{2}m\omega^2 x^2$) in which it's stated that the probability of finding the particle in the $\psi_0$ ...
- 77
2
votes
1
answer
140
views
Transformation of wavefunction
While learning QM, I was wondering how would the wavefunction of a particle, suppose charged particle, look for different observers moving with respect to each other.
To begin with, let the electric ...
- 426
-1
votes
1
answer
89
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How to calculate the inner product $ \langle T|x \rangle = \langle\frac{p^2}{2\mu} |x\rangle$? [closed]
If I have a wave function $ \psi (x) = \langle x|\psi \rangle$, now I want to use kinetic energy representation $$ T = \frac{p^2}{2\mu} ,$$ where $ \mu $ is the mass of particle. I try to
\begin{align*...
- 37
0
votes
1
answer
80
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Momentum Eigenvalues for Particle in a Box
A question from my college exams is as follows:
Find out the eigenfunctions and eigenvalues of the momentum of a particle of mass $m$ moving
inside an infinite one-dimensional potential well of width ...
- 143
1
vote
0
answers
69
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Evaluation of $\langle nlm|\frac{1}{r^2}|nlm\rangle$ [closed]
I am trying to prove that $$⟨nlm|\frac{1}{𝑟^2}|nlm⟩=\frac{1}{𝑛^3*𝑎^2*(l+\frac{1}{2})}$$
(where $𝑎$ is the Bohr radius) for the $|𝑛𝑙𝑚⟩$ state of hydrogen. I know how to do this using Hellmann–...
- 11
0
votes
1
answer
47
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How do I find the wavefunction equation for a translated potential? [closed]
Let me explain myself. In my case, I know the wavefunction equation of a infinite-U potential which has the form:
$$V(x)=\begin{cases} V_0,\ \ |x|\leq \frac a2\\ \infty, \ \ |x|>\frac a2\end{cases}$...
- 75
1
vote
1
answer
74
views
Infinite potential well suddenly expanding
Problem statement: an electron is in its fundamental state in an infinite (1-dimensional) potential well, its walls being located at $x=0$ and $x=a$. Suddenly, the right wall moves from $x=a$ to $x=2a$...
- 1,616
1
vote
1
answer
144
views
How to solve for a particle in a triangular well? [closed]
I am currently trying to solve the problem of a particle confined within an infinite well subject to a linear electric field (i.e. triangular well). This entails solving the Schrodinger equation
$$-\...
- 181
1
vote
0
answers
95
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Does this question make sense?
I currently have a question in a Quantum Mechanics course, which doesn't seem like it makes sense to solve. I obviously am not looking for a solution, but I want to check if it is even possible with ...
- 11
0
votes
1
answer
198
views
Semi-infinite potential well with $E<-V_0$
I'm struggling with the following problem:
Consider the semi-infinite potential well with equation:
$$ V(x) = \begin{cases} +\infty & x<0 \\ -V_0 & 0<x<a \\ 0 & x>a \end{cases}$...
0
votes
1
answer
126
views
Solutions for an electron near a 1D Coulomb
I am only a amateur solving the time-independent Schrödinger equation, and I only know how to solve the 1D box. When I went to search up more realistic examples, i.e. the Coulomb well, no one seemed ...
0
votes
1
answer
72
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How we construct the Gaussian wave packet at $t=0$ with given avarage coordinate and momentum? Does it satisfy any Schrödinger equation? [duplicate]
I've begun delving into quantum mechanics and encountered a point of confusion. In classical mechanics, we define an initial position and initial momentum, which can take on any values. However, in ...
- 1
0
votes
1
answer
198
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Gaussian wave packet time evolution
I am currently studying quantum mechanics and I am struggling to obtain the time evolution of a Gaussian wave packet.
We know that the wave function of a free particle is:
$$\Psi(x,t)=\frac{\sqrt{a}}{(...
- 81
0
votes
1
answer
179
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Probability current density of gaussian wavepacket
This was the question that was asked in an exam.
For a gaussian wavepacket $$ \psi(x,t) = Ae^{\frac{x^2}{4a^2}}e^{i(k_0x-\omega_0t)} $$ corresponding to a free particle, (i) Find the probaibility ...
- 353
0
votes
2
answers
80
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Can two normal 1D waves form a wave packet?
I have a confusion
A wave packet is described by the superposition of two wave functions: $$Ψ_1(x,t)=A\sin(k_1x−ω_1t)$$ and $$Ψ_2(x,t)=A\sin(k_2x−ω_2t),$$ where $k_1=2.0×10^6\text{m}^{−1}$, $k_2=3.0×...
