I was referring to ψβ as the overall superposition of all the possible states. Ergo, the bound state added to the free particle states. Notice that the problem itself doesn't specify exactly what ψβ is; it only tells me what the new potential function is.
It's also possible that I'm a bit...
It's a delta function. There is no width. While it is in a bound state, you are right. However, if the potential suddenly changes to some other value, then there is a chance that it moves off.
I am not sure how time is involved. When I tried to include time while treating it as a free particle...
Homework Statement
I have a particle which is initially in a bound state for a given voltage in the form of a delta function at the origin,
V = -αδ(x)
initial state is ψα = (√αm)/h2*exp(-m*α*|x|/(h2)
At t=0, voltage is changed to V = -βδ(x)
both α and β are greater than zero. Right now I'm...
I guess I should've been more descriptive. I have all that information already (even though this is for spherical coordinates and not polar). The equation I got for the last term multiplied by R is mu*r^2. This is why I'm having trouble, since it doesn't really agree completely with the normal...
Homework Statement
A solid ball at 30 degrees C with radius a=1 is placed in a refrigerator that maintains a constant temperature of 0 degrees C. Take c (speed)=1 and determine the temperature u(r,theta,phi,t) inside the ball
Homework Equations
partial differential heat equation in...