Quantum mechanics I Fall 2012 Physics 451 Quantum mechanics I Fall 2012 Oct 1, 2012 Karine Chesnel

HW # 9 due Tuesday Oct 4 by 7pm Pb 2.27, 2.29, 2.30, 2.31 Quantum mechanics Announcements Homework this week: HW # 9 due Tuesday Oct 4 by 7pm Pb 2.27, 2.29, 2.30, 2.31 HW # 10 due Thursday Oct 7 by 7pm

The delta function potential Ch 2.5 Quantum mechanics The delta function potential For Continuity at boundaries is continuous is continuous except where V is infinite

The delta function well Ch 2.5 Quantum mechanics The delta function well Bound state Pb 2.27 double delta well 2 boundaries, 4 conditions

The delta function well Ch 2.5 Quantum mechanics The delta function well Scattering state x Travelling waves A B F G Continuity at boundary (A,B, F,G) ?

The delta function well Ch 2.5 Quantum mechanics The delta function well Scattering state A F B x Travelling waves Reflected wave Transmitted wave

The delta function well Ch 2.5 Quantum mechanics The delta function well Scattering state A F B x Reflection coefficient Transmission coefficient

The delta function potential Ch 2.5 Quantum mechanics The delta function potential Scattering state

The delta function barrier Ch 2.5 Quantum mechanics The delta function barrier Scattering state only A F B x “Tunneling” Reflection coefficient Transmission coefficient

Quiz 13 Quantum mechanics A particle can tunnel trough an infinite barrier with some relatively small thickness Yes No

The finite square well Quantum mechanics V(x) Scattering states -a a x Bound states -V0

The finite square well Quantum mechanics V(x) x -V0 Ch 2.6 Continuity at boundaries V(x) x -V0 is continuous X=+a X=-a

Ch 2.6 Quantum mechanics The finite square well Bound state For For

The finite square well Quantum mechanics Ch 2.6 Bound state For General solution

The finite square well Quantum mechanics x -V0 Pb 2.30 normalization Symmetry considerations V(x) The potential is even function about x=0 The solutions are either even or odd! x -V0 Pb 2.30 normalization

The finite square well Quantum mechanics x -V0 Continuity at boundaries V(x) x -V0 Continuity of

Quantum mechanics The finite square well Bound states where

The finite square well Quantum mechanics V(x) V(x) x x -V0 -V0 Bound states V(x) x -V0 Wide, deep well large (large a or V0) Shallow, narrow well V(x) x -V0 small (small a, V0) One bound state Pb 2.29 odd solution Pb 2.31 extrapolation to infinite delta well