Question

Can anyone help me to solve this question on Quantum Mechanics about Schrodinger equation please?

1. (a) From the definitions of probability density and flux, P(x,t) = 4*(x,t){(x,t) (:9 = 2 show that ƏP(x,t) at @j(x,t) Ox GP(x,t) for a particle satisfying the Schrodinger equation iħ – I hº o°F(x,t). ?+V(x)*(x,t) am Ox? at provided that the potential V(x) is real..

Answer 1

9. Anscer 4 = 4 Exit P(x, f1 = 4*(x, f 14 (x, f) & j czt? = h ( 44 24 4 aut 7 911111111111 it dyrxt1 dt t² 22 2ucxth 3 4 ( xefl +varu cat] zm Now d x2 aj (3,4) + Tayt dy - 434 - * 2 P dza and a pcx,f} = 4*4 + 24 4 dt - Noa alle dx at L ot of 7 - QE Nem adding ① to, we have DJ (x,t) a pixit? 524td 4 - ZimL da da - t ut ly + h 4 3 4 4 +48 94 + 24*4 Now, using Schrödingen was equation, we have 24 = - h 24 at zim 2x2 ir - + b 2 4* + valy at - zim doc? Fin zim dxz 'zim dx2 Zim 2002 tv (x) 4 of JW* * Y) = 30 avajcars) + BP CAD 0- da at 34 x3y2v OT . im dac? Zin da? Zim dx² + Vex? y y + ħ 4 84* - Vix) 447 1h zim ax² 1h.

ajlat) Japcait) - ax a t o-o- o + V (27 ustup - vext y ý 1h Since nor is real, so so Vexi = vcxo* & 144*1 = 14441 aj (2447 + 2 plant) - o axat Tapet? __DJ (xit? at - 2x -