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Tagged with homework-and-exercisesschroedinger-equation
517 questions
7votes
2answers
543views
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
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: $$ E = \frac{h^2}{...
- 57
1vote
2answers
80views
Griffiths and Schroeter: Transformation of operators
In Example 6.1 of Griffiths and Schroeter,Introduction to Quantum Mechanics (3rd Edition) suggest determining the transformation properties of the operator $\hat{x}$ by the translation operator $\hat{...
- 3,934
1vote
3answers
114views
Infinite Well when particle is on one side
Suppose in a infinite well from $-a$ to $a$ we make a measurement and find out that the particle is in $0$ to a at time $t$. I had a really hard time figuring out what exactly is happening here do the ...
- 362
1vote
1answer
104views
Placing delta potential at the boundary of infinite well
If the walls are at $x=0$, $x=L$, then I place a attractive delta potential at $x=0$, that is $-g\delta(x)$. Then what will happen to the eigenstate? One will have $$\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$$\varphi(k)=\sqrt{\frac{1}{2\pi L}}\int^...
- 135
0votes
1answer
79views
Study evolution of particle in infinite square well, with the walls suddenly removed [closed]
$V(x)=\infty$ at $x=\pm L$ and $V=0$ for $|x|\leq L$ then consider the ground state$$\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 ...
0votes
1answer
59views
1D 2-step finite square potential barrier [closed]
I need to solve this problem. Given a one dimensional 2 step potential barrier and have to write the time-independent Schrödinger equation for the 4 intervals. Before zero, from zero to a, from a to ...
- 11
1vote
0answers
78views
Derivation of SECOND-order time-dependent perturbation theory (TDPT)
Are there any detailed derivation of the second oder term of TDPT? I found a pdf note on google, but an important equation in this pdf maybe wrong. How can I get (17) from (15) and (16)? It seems ...
