What Are the Conditions for a Particle in a Bound State of a Potential Well?

[bon]

Homework Statement

State three conditions that must be satisfied by the wave-function of a particle that is in a bound state of a potential well.

Homework Equations

The Attempt at a Solution

Not sure what the three are!?
I can only think of one: the wavefunction must be continuous.

The derivative doesn't necessarily need to be continuous does it? e.g. in delta function potential well it isnt..

Also it doesn't need to vanish at the ends of the well does it--this is only for an infinite well..

so what are the other two?


Thanks!

 

[Disconnected]

Homework Statement

State three conditions that must be satisfied by the wave-function of a particle that is in a bound state of a potential well.

Homework Equations

The Attempt at a Solution

Not sure what the three are!?
I can only think of one: the wavefunction must be continuous.

The derivative doesn't necessarily need to be continuous does it? e.g. in delta function potential well it isnt..

Also it doesn't need to vanish at the ends of the well does it--this is only for an infinite well..

so what are the other two?


Thanks!

The only other ones I can think of is the wave-function must be normalized so the total probability is 1, and that it has to tend to the classical limit.

 

[chrisbaird]

Bound states are stationary states, meaning that apart from a trivial harmonic time dependence, the wavefunction does not change shape over time. What this also means is that apart from the harmonic time factor, the wavefunction is real-valued, whereas wavefunctions in general are complex-valued.