# Tag Info

### B.C. for time-decaying delta barrier inside an infinite well

To solve the time-dependent Schrödinger equation for the infinite well with the given potential, we need to apply the boundary conditions and the conditions imposed by the delta potential. Let's go ...

### Numerically Solving the Schrödinger Equation for Coulombic Barrier in Fusion

Solving the Time-Dependent Schrödinger Equation for the Tunneling Problem in Fusion Processes Problem Statement The time-dependent Schrödinger equation (TDSE) for a particle of mass ( m ) encountering ...
1 vote
Accepted

### Plane waves, angular momentum, and the 2D Schrödinger equation

I believe the answer to your question is simply that plane waves are not angular momentum eigenfunctions, as a direct calculation shows: \begin{align} (x\partial_y - y\partial_x)e^{ik_x x+ ik_y y} = (...
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### On using Python to solve Time Independent Schrodinger Equation, the eigenfunctions have their values "pushed" to one of the boundaries?

You may want to try out a new approach: "The Phase Method" (http://gbxafs.iit.edu/phase-method). It can easily solve your problem, and others of this type.
1 vote
Accepted

### Reflection of quantum particle colliding with a potential barrier

Your last statement is basically correct. For a single particle, the current $\vec{J}$ is measuring a current of probability density $|\psi|^2$. However, to physically interpret what such a ...
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### Are reflection and transmission coefficients in 1D problem are independent of the direction in which we choose as incident?

In general the reflection and transmission coefficients are not independent of direction for arbitrary potentials. For a discussion of the conditions under which the transmission coefficient is ...
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1 vote

### Are reflection and transmission coefficients in 1D problem are independent of the direction in which we choose as incident?

You are right. There is some symmetry, but only enough to relate $T$ and $T'$, not to get $R=R'$. You can even find this as a classical result: (for light or EM waves, or electrical signals) https://...
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Accepted

### Am I reading the Madelung equations for a 1D quantum particle right?

Did you verify your TDSE, dimensionally? Your S, here, atypically, is an action over ℏ, hence dimensionless, $\psi\equiv R e^{iS}$; it produces the well-known continuity and quantum Hamilton-Jacobi ...
• 63.4k
1 vote
Accepted

### Quantum Harmonic Oscillator With a Linear "Perturbation"

Your main idea is right: it is a matter of making a change of variables. But I think you made a change of variables that could be slightly improved. If I didn't mess up any calculations (please double ...
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