08square - Finite Square Well Potential For V=finite...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
P460 - square well 1 Finite Square Well Potential • For V=finite “outside” the well. Solutions to S.E. inside the well the same. Have different outside. The boundary conditions (wavefunction and its derivative continuous) give quantization for E<V 0 • longer wavelength, lower Energy. Finite number of energy levels • Outside: h h h h ) ( 2 2 ) ( 2 0 2 ) ( 0 0 2 2 2 0 2 2 2 ) ( cos , sin ) ( E V m x k V E m m k dx d m k e V E k V E and k x k V E V E ± = < = = > = ψ h mE k 2 1 =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
P460 - square well 2 Boundary Condition • Want wavefunction and its derivative to be continuous • often a symmetry such that solution at +a also gives one at -a • Often can do the ratio (see book) and that can simplify the algebra x boundary x boundary x boundary x boundary boundary boundary = = = + + + + ) ( 1 ) ( 1 ) ( ) ( ) ( ) ( ψ
Background image of page 2
P460 - square well 3 Finite Square Well Potential 0 , 0 ) ( : ) ( : cos sin ) ( : 2 2 2 2 2 2 1 1 = ±∞ + = > + = < + = F D x as as Ge Fe x x De Ce x x x k B x k A x inside x k x k a x k x k a ψ Equate wave function at boundaries 2 / 2 2 2 / 2 2 2 1 1 2 1 1 cos sin cos sin a k a k a k a k a k a k Ce B A Ge B A = + = + And derivative 2 / 2 2 1 2 1 2 / 2 2 1 2 1 2 1 1 2 1 1 sin cos sin cos a k a k a k a k a k a k e Gk Bk Ak e Ck Bk Ak = = +
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
P460 - square well 4 Finite Square Well Potential on quantizati k k x e e B x well in x k B x II on quantizati k k x e e A x well in x k A x I a k a x k a k a k a k a x k a k a k 2 2 1 2 2 / 2 1 2 2 1 2 2 / 2 1 1 2 2 1 1 2 2 1 tan ) cos( ) ( cos ) ( : cot ) sin( ) ( sin ) ( : = > = = = > = = ψ E+R does algebra. 2 classes. Solve numerically k1 and k2 both depend on E. Quantization sets allowed energy levels 0 2 2 2 2 2 V E ma n n π h
Background image of page 4
P460 - square well 5 Finite Square Well Potential Number of bound states is finite. Calculate assuming “infinite” well energies. Get n. Add 1 Electron V=100 eV width=0.2 nm 2 2 0 2 2 2 2 2 2 2 0 2 π h h V ma ma n n n V E ) ( 4 7 . 10 2 2 2 ) 14 . 3 ( ) 197 ( 100 ) 2 (. 51 . 2 2 levels of number
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/02/2009 for the course PHYS 460 taught by Professor Johnson,c during the Spring '08 term at Northern Illinois University.

Page1 / 22

08square - Finite Square Well Potential For V=finite...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online