Question

Quantum Mechanics question about an infinite square well.

A particle in an infinite square well potential has an initial state vector 14() = E1) - %|E2) where E) is the n'th eigenfunctions of the Hamiltonian operator. (a) Find the time evolution of the state vector. (b) Find the expectation value of the position as a function of time.

Answer 1

(81678 167 21 167 as ņ En> = En / End of length L. particle. for one D box u=mass of n En = 20122 iĥt was à 17 h 141037 14 (4) = - t exp(-26€) 15> - ' CXPL164)157 1 <440) - topp (194) <0.) + af enp (**) <6] <90))*141457 , 2612197 + < (6/2/637 - din exp [169pt) <6121627 + ai exp ( :(t2-6)t) < E21 x 1 G7 S 167 = sin IX OLALL since OLXCL - OCXLL 1972 E sin ar (En 1x1 Em7 = 2 Inity sin mix dx

for men Elx/Em7 - I cxflos - Los (ritm) ITR ( da tor As for any nez ( T) » (2 (EN 1001 Em7 -Ź - 11-4) 1) - 22-10) / 17 (n-m)?n? (htm) ²2 so for man 30, for Enlx/En7 = 2 ( x sinnite da - ? S e(1- Cos 20172) de cosanin sin anipal - in b ran 20 h as sinnico, cosant al, for nez + 4 x t - ai 1976 7 L4 Lt)/x/4 47 = 1 b the d + 2 ) 2 2 [ + - + J + aj exp (i(5, 674) *

24 18/12/ - 248 RP (exp('06-07*) _cxplicar 9 T12 - 324 si sin (63-6 7 2 7572 t I sin 64 4572 ( 3 T ht 7 I QML2J As &- G = (4-1) I h = 3722 제2 2M22