7-Potential steps and barriers

make notes on 7.3,

What is the Time-Independent Schrödinger Equation (TISE) for a free particle travelling in a constant potential?

What is the general solution to the TISE for a free particle travelling in a constant potential?

What is the general solution to the Time-Dependent Schrödinger Equation (TDSE) for a free particle travelling in a constant potential??

What is the probability density ρ(x,t) of a particle with wavefunction ψ(x,t) travelling in the positive x-direction?

What does the probability density ρ(x,t)=A² indicate about the particle's location?

• The probability density is constant in time and uniform in space

• This means the particle is equally likely to be found anywhere.

Why is the probability density uniform for a travelling wave?

Because the wavefunction represents a free particle not confined by a potential, so there is no preferred location.

What is the potential function V(x) for a particle encountering a potential step (sudden change in potential)?

Continue from 7.4