Slide 101 * Outline The infinite square well A comment on wavefunctions at boundaries Parity How to solve the Schroedinger Equation in momentum space Please read Goswami Chapter 6 Finite case Infinite[.]
Outline I.The infinite square well II A comment on wavefunctions at boundaries III.Parity IV.How to solve the Schroedinger Equation in momentum space Please read Goswami Chapter I The infinite square well Suppose that the sides of the finite square well are extended to infinity: It is a simplified case of the finite square well How they differ: Finite case Infinite case (1)Since V is not infinite in Regions and 3, it is possible to have small damped ψ there terminate Since V is infinite in Regions and III, no ψ can exist there ψ must abruptly at the boundaries Finite case Infinite case To find the ψ’s use the boundary conditions The abrupt termination of the wavefunction is nonphysical, but it is called for by this (also nonphysical) well Abrupt change: we cannot require dψ/dx to be continuous at boundaries Instead, replace the boundary conditions with: Result: ψ = B cos k1 x or A sin k1 x Solve for ψ in Region only Begin with ψ = Acoskx + Bsinkx but require ψ = at x = ± a/2 Result: ψ2 = sin k n x (n = 2,4,6, ) a (A and B are complicated) k1 = 2mE h E is sol'n of a transcendental equation cos k n x (n = 1,3,5, ) or a k1 = 2mE nπ = h a π 2h n E= 2ma (n = 1,2,3 ) II Comment on wavefunctions at boundaries Anytime a wave approaches a change in potential, the wave has some probability of reflecting, regardless of whether its E is >V or