Tagged Questions

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Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
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Numerical solving of 2D and 3D Schrodinger equations

I am studying 2D quantum scattering models for my Bachelor's thesis. Somewhat like these: ,with Dirichlet ($\psi \mid_\Gamma = 0$) boundary conditions on the "walls" of the waveguide and the ...
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I am trying to understand some points about the paradox, what I am doing is solving the for the step potential $$V = V_0 ~\theta(z)$$ I have two solutions $$\Phi_I = e^{ik_1 z} + r e^{-ik_1 z}$$ ...
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Solving the 1-d time-independent Schroedinger's equation with an infinite boundary

In my introductory modern physics class we have examined time-independent solutions to the SchrÃ¶dinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...
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Radial Wave Function for Spherical Squared Well Potential and $S$-Matrix

I have a problem with this exercise because I really don't know how to proceed. It's related with the "S-matrix". In class we saw this example: Consider the spherically symmetric potential: ...
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Transparence of an infinite square well? [closed]

What does it mean by an infinite square well being transparent? I have been doing the calculation of the infinite square well and I came up with an answer $T = 1$ where $T$ for Transmission ...
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QM Question about the Dirac Delta Potential

I just wrote down the solution for the bound state of the Dirac delta potential well, for $E<0$, and apparently there is only one specific energy for the bound state, and it is negative. I solved ...
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Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$

Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients ...
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Tunneling and transmission

Lets say we have a tunelling problem in the picture, where $W_p$ is a finite potential step: If particle is comming from the left a general solutions to the SchrÃ¶dinger equations for sepparate ...
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Potential step and its transmission / reflection

Lets say we have a potential step with regions 1 with zero potential $W_p\!=\!0$ (this is a free particle) and region 2 with potential $W_p$. Wave functions in this case are: \begin{align} ...
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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 ...
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Why is the energy spectrum continuous for a plane wave when it has energy less than the potential barrier?

Please explain it in the context of this task: we have a potential barrier that looks like $\prod$, with $E<U$. There are 3 regions: 1) no field 2) barrier 3) no field Solution could be ...
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Electron Incident On A Finite Potential Barrier

This is problem 2.8.3 from Miller's Quantum Mechanics For Scientists And Engineers. I'm getting stuck when I try to figure out the wave equation on the right-hand side of the barrier. The original ...
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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 ...
Why are these states called as such, and how do they differ? I vaguely understand that when $E > 0$ you obtain a scattering state, but when $E < 0$ you have a bound state.