2
votes
0answers
36 views

Self-adjoint extensions with 'teletransporting' boundary conditions

When choosing a self-adjoint extension of a Hamiltonian, in general one can obtain domains in which (i) the probabilities teleport* between points on the boundary and (ii) boundary conditions ...
2
votes
1answer
55 views

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 Schrödinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...
4
votes
3answers
410 views

Comparison of 1D and 3D wave functions

When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy ...
3
votes
5answers
727 views

Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
1
vote
2answers
164 views

Complex Versus Real Wave Velocities in Quantum Mechanics

There's a fantastic quote in Schrodinger's second 1926 paper1 that apparently provides some motivation for the discrete energy levels (I think) that I'm having trouble interpreting: I would not ...
2
votes
1answer
451 views

How to solve bound states of 2D finite rectangular square well?

I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well \begin{equation}V(x,y)=\cases{0,&$ |x|\le a ...
0
votes
1answer
1k views

Periodic boundary condition on a Wave Function of a Particle in a Box

Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
1
vote
1answer
279 views

What's the average position of oscillating particles in a box with periodic boundary conditions?

Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D). Now put a ...
3
votes
4answers
783 views

Is the momentum operator well-defined in the basis of standing waves?

Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely $$ \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
1
vote
2answers
1k 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 ...
6
votes
1answer
257 views

Quantum Field Theory: why fields are equal to zero on the boundary?

One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is $$ \phi(x)=0\,\text{on the boundary} $$ and this is widely used in many situations ...
3
votes
2answers
337 views

Boundary conditions for crystals

As students on solid state physics, we are all taught to use the periodic boundary condition, taking 1D as an example: $\psi(x)=\psi(x+L)$ where $L$ is the length of the 1D crystal. My question is: ...
2
votes
2answers
494 views

Can we impose a boundary condition on the derivative of the wavefunction through the physical assumptions?

Consider the Schrödinger equation for a particle in one dimension, where we have at least one boundary in the system (say the boundary is at $x=0$ and we are solving for $x>0$). Sometimes we want ...
0
votes
0answers
262 views

boundary conditions

let be the operator $ -i\hbar x\frac{df(x)}{dx}-i\hbar \frac{f(x)}{2}=E_{n}f(x)$ what kind of bundary conditions can i put ?? i have tried to find a function so for every integer 'n' i get $ ...
9
votes
2answers
384 views

When “unphysical” solutions are not actually unphysical

When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity: ...