Chapter 4 Flashcards
Be able to solve the TISE in regions of constant potential to show that the solutions are
• Know that in the case where E > V0 an alternate form for the general solution (useful for bound state problems) is
ψ(x) = A cos kx + B sin kx when E > V0
Know how to apply these boundary conditions together with the boundary conditions of continuity and continuity of the first derivative to solve problems:
Infinite square well
Know how to apply these boundary conditions together with the boundary conditions of continuity and continuity of the first derivative to solve problems:
Finite Square well
Know how to apply these boundary conditions together with the boundary conditions of continuity and continuity of the first derivative to solve problems:
Potential step (E<0)
Know how to apply these boundary conditions together with the boundary conditions of continuity and continuity of the first derivative to solve problems:
Potential step (E>V)
Know how to apply these boundary conditions together with the boundary conditions of continuity and continuity of the first derivative to solve problems:
Potential Barrier
Be able to derive the equation for particle flux
Be able to describe the properties of the eigenfunctions and eigenvalues (energy levels) of the quantum harmonic oscillator, i.e., that the wave functions are the product of a Hermite polynomial and a Gaussian function and that the energy levels are quantised by
• Be able to derive the following equation for first order corrections to the energy eigenvalues given a small perturbation to the Hamiltonian
• Be able to apply this equation calculate the first order energy corrections for model systems.
Tunnelling example 1
Tunnelling example 2
when to use little k and no i
when E<v>
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