Tagged Questions
0
votes
2answers
55 views
Electron in an infinite potential well
Does this problem have any sense?
Suppose an electron in an infinite well of length $0.5nm$. The state of the system is the superposition of the ground state and the first excited state. Find the ...
0
votes
0answers
43 views
Wave equations for two intervals at Potential step
Lets say we have a potential step as in the picture:
In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$.
Let me ...
0
votes
1answer
97 views
Energies and numbers of bound states in finite potential well
Hello I understand how to approach finite potential well (I learned a lot in my other topic here). However i am disturbed by equation which describes number of states $N$ for a finite potential well (
...
2
votes
2answers
280 views
Plotting $\psi$ for finite square well potential
Lets say we have a finite square potential well like below:
This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
1
vote
1answer
109 views
Finite potential well - transcendent equation for even solutions
I have a finite square well like the one on the picture below:
I have done some calculations on it and got a transcendental equation for even solutions which is like this:
$$
...
1
vote
1answer
146 views
Finite, square, potential well
Lets say we have a finite square well symetric around $y$ axis (picture below).
I know how and why general solutions to the second order ODE (stationary Schrödinger equation) are as follows for ...
1
vote
2answers
460 views
Particle in infinite potential well which is doubled in size at $t_0$
I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding.
The Problem:
A Particle sits in an infinite potential well ...
1
vote
1answer
186 views
Does a particle in a spherically symmetric infinite square well potential exert a force on the inner and outer shell barrier?
For a particle in the potential:
$$V(r) =
\begin{cases}
0 & \text{a < r < b}\\
\infty & \text{otherwise.}
\end{cases}$$
Does this guy in the ground-state exert a force on the shells a ...
1
vote
2answers
493 views
Barrier in an infinite double well
I am stuck on a QM homework problem. The setup is this:
(To be clear, the potential in the left and rightmost regions is $0$ while the potential in the center region is $V_0$, and the wavefunction ...
0
votes
1answer
82 views
a positive potential as $ x \rightarrow \infty $
let us suppose i can calculate the asymptotic of any potential $ V(x) $ in one dimension , and that i manage to prove that $ V(x) \ge 0 $ as $ x \rightarrow \infty $
could i conclude taht if or big ...
5
votes
2answers
127 views
Is there a time delay during tunnelling?
A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
3
votes
3answers
355 views
Can we have discontinuous wavefunctions in the Infinite Square well?
The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
1
vote
0answers
340 views
Scattering on delta function potential
Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$.
How can one show or explain that ...
0
votes
1answer
347 views
Bound states for sech-squared potential
I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated.
My goal is to determine the bound states and their ...
5
votes
1answer
108 views
Apparent contradiction between calculations and intuition?
I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with.
We have a potential step ...
2
votes
2answers
187 views
Classical limit of a quantum system
If we have a one dimensional system where the potential
$$V~=~\begin{cases}\infty & |x|\geq d, \\ a\delta(x) &|x|<d, \end{cases}$$
where $a,d >0$ are positive constants, what then is ...
2
votes
1answer
805 views
How to solve Schrodinger Equation - Tunnelling
I have to solve analitically the Schrodinger equation in one-dimension with a barrier of potential (tunnel effect):
$$ih \frac{d}{dt} U(x,t) = \left[ \left(-h^2 \frac{d^2}{dx^2} \right) + q V(x) ...
3
votes
1answer
299 views
Can we solve the particle in an infinite well in QM using creation and annihilation operators?
The particle in an infinite potential well in QM is usually solved by easily solving Schrodinger differential equation. On the other hand particle in the harmonic oscillator oscillator potential can ...
-1
votes
2answers
141 views
Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]
A particle of mass m moves on the x-axis under the influence of the potential
$$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$
Can anyone help me, using Schrödinger's equation in one dimension that the energy ...
2
votes
1answer
762 views
How to calculate time evolution of a wave function in an 1D infinite square well potential?
A particle in an infinite square well has an initial wavefunction
$$\psi (x,0) ~=~ Ax(a-x) \qquad \mathrm{for}\qquad 0\leq x\leq a.$$
Now the question is to calculate $\psi (x,t)$.
I have ...
1
vote
1answer
240 views
A quantum particle in a box (with a catch)
I am reading Shankar's Quantum Mechanics and I am looking at the case where there is one particle inside a box, where the potential is zero inside the wall and abruptly goes to infinity outside the ...
20
votes
4answers
756 views
In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?
A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential.
Is there a one to one correspondence between the potential and its spectrum?
If the ...
14
votes
6answers
950 views
Why can we treat quantum scattering problems as time-independent?
From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:
Solve the time-independent Schrodinger ...
