Question

2) For the given equations: V(z) = { é o se} V(,0) = V $(x) + V1() + vee(r) a) Write the expression for 4A (x,t). b) What is the expectation value for (E) ? Write the expression in E.. c) Write the expression for W.(x,t) at E2 for t>t, and what is the probabilities at t2 > ti d) Write the another expression for WB(x, 0) with the same value of (E). e) Write the another expression for c(x,0) with the same value of (E), but E1 = 0, and then calculate P(E.) and P(E2)

Answer 1

Solution 4cv = p sin (TL) wave function and the energy eigenvalue is Vlu I fn = n²² h 2 - am L2 YA (2,0) = Ę pocx) + Tag 09 () + 4, 6%) (Given) do(w = Ground Stade = Ę sin 1 107 = r sin 2721 Similarly ... to = (2) 2 7 2 2 2 = 1²h2.. 2 ml 97² 72 fo- , F2 = am 22 1 = 27²72 mo z - Ezt 1. leot ñ ħ 1 3 da 6x7 e b.(012 e 7 YA (ast) = J + 42.699 e 264

given that metal sphere Enlution' - Tt is (b) El = 480 ; Ez = geo KES = 6)? 6o + () 9€ + ta)*9€. = Eo ( + + 2) = 6f. Ang PACA ) = 2017 (49 € - 96. 4862130) = Edera + 4,130) + Š $2000), o when t in look like some ' as Y AC2,0) <E) = GEO (same) @ Ucud) = 4810120) = to 40() + 4,(9)+'40(0) Preo) = 6 + 2 = 7 PIE2) = 6) =