All Questions
536 questions
7votes
2answers
562views
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 $$-\...
- 281
0votes
0answers
45views
Request for help deriving wave function for Hydrogen (FLP Vol. III Eq. 19.30) [closed]
Basically, I've been going slightly mad for three days trying to derive one of the equations from the Feynman's course, namely eq. 19.30 from Vol.3, or the spherically symm. wave function for H at the ...
- 1
1vote
0answers
43views
Existence of bound state in semi-infinite potential [closed]
We consider the bound states of a particle in the following asymmetric finite potential well: $$ V_B(x) = \begin{cases} 0 & (x < a) \quad \text{(Region I)} \\ - V_0 & (a \leq x \leq b) \...
- 405
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
1vote
3answers
114views
Infinite Well when particle is on one side
Suppose in a infinite well from $-a$ to $a$ we make a measurement and find out that the particle is in $0$ to a at time $t$. I had a really hard time figuring out what exactly is happening here do the ...
- 362
2votes
0answers
82views
A Problem In Using Heaviside And Dirac Distributions To Calculate Uncertainties [closed]
Edit: As @Andrew very accurately pointed out below, I did not calculate $\Delta x$ and $\Delta k$ correctly! The following is from Zettili's Quantum Mechanics, Problem 1.11. Find the Fourier ...
- 29
1vote
1answer
104views
Placing delta potential at the boundary of infinite well
If the walls are at $x=0$, $x=L$, then I place a attractive delta potential at $x=0$, that is $-g\delta(x)$. Then what will happen to the eigenstate? One will have $$\psi'_{+}(0)-\psi_{-}'(0)=-\frac{...
- 135
6votes
1answer
277views
Understanding time evolution of a particle in infinite square with collapse walls
Suppose the width is $2L$, then the ground sate wavefunction within the well $$\psi(x)=\sqrt{\frac{1}{L}}\cos\frac{\pi x}{2L}$$ then the momentum representation$$\varphi(k)=\sqrt{\frac{1}{2\pi L}}\int^...
- 135
1vote
2answers
114views
Translation operator with phase factor
I have a question that is mainly about Bra-ket notation. We usually define the translation operator via: \begin{align}\tag{1}\label{1} T_\epsilon |x \rangle = |x +\epsilon \rangle. \end{align} We can ...
- 141
0votes
1answer
79views
Study evolution of particle in infinite square well, with the walls suddenly removed [closed]
$V(x)=\infty$ at $x=\pm L$ and $V=0$ for $|x|\leq L$ then consider the ground state$$\psi(x)=\sqrt{\frac{1}{L}}\cos\frac{\pi x}{2L}$$ notice the width is $2L$. The energy is $E=\frac{\hbar^2\pi^2}{8mL^...
- 135
3votes
0answers
88views
Harmonic oscillator confined in an even infinite square well [duplicate]
Suppose we have a harmonic oscillator confined in an even infinite square well with width $2a$. The potential is given by $V(x) = \frac{1}{2} m \omega^2x^2, -a<x<a$ and $V(x) \to \infty, x<-a ...
1vote
0answers
95views
Free particle with time evolution $\sqrt{\frac{m}{m+i\hbar t(2i \alpha+1)}}\exp\left[\frac{ik^2m}{2(\frac{m\sigma^2}{i\alpha'}-\hbar t))}\right]$
I calculated the time evolution of the free particle $$\psi(x,0)=A\exp(-x^2/2\sigma^2)\exp(i\alpha x^2),$$ with a positive real parameter $\alpha>0$. $$\Psi(x,t)=A\sigma\sqrt{\frac{m}{m\sigma^2+i\...
- 135
0votes
2answers
138views
Proof of nodes of bound states using the wronskian
I've been trying to solve this problem for a couple of weeks now, but I don't seem to get nowhere with it. I tried to prove it by contradiction, supposing $\psi_q$ has no nodes, and finding some ...
user461831
0votes
1answer
95views
Approximation to the differential equation $\dfrac{d^2\psi}{d \xi^2} = \xi^2 \psi$ for large values of $\xi$
I'm interested in understanding the approximate solution for large values of $\xi$ (as $\xi \rightarrow \infty$) of the following differential equation $$\dfrac{d^2\psi}{d \xi^2} = \xi^2 \psi$$ which ...
