Let (t, x) = = 1 (1) with o(t) = of+i and oo > 0. 00 2m (i) Show that (t, x) is a solution

Let

(t, x) = = 1 ασ(1)

with o(t) = of+i and oo > 0. 00 2m

(i) Show that (t, x) is a solution of the free, one-dimensional, time-dependent Schrödinger equation

ih მ (t, x) h2 02 2m x2 (t, x).

(ii) Determine a such that for all t≥ 0 it follows da v(t, x)|² = 1. (iii) Calculate the probability current density

(v(t, x)* (t, x) – (t, x) (t, x)"). j(t, x) = ; 3 – 2mi

Remark:

L dye-y² = √π