An infinite square well confines a particle of mass m to the region -a/2

An infinite square well confines a particle of mass m to the region -a/2 < x < a/2. The particles spatial wave functions can be written: An infinite square well confines a particle of mass m to the region a/ 2 < < a/2. (This well is shifted compared to the one considered in class.) The particle's spatial wave functions can be written 2 nnx for n = 1, 3, 5,..., cos a a 2 nnx sin '2x cos 2x sin a for n = 2, 4, 6, .... a Therefore, en a relationship that holds [with (1)n 1 replaced by (1)n in cases where the ground state is labeled n = 0 rather than n = 1] for any potential satisfying V@). sin2 + cos2 1, 2 sin cosy sin@y) + sin@+y) 2 sin sin y = cos@y) + cos@+y), sin c dc sinc a; cos x, cos @22) sin c + 2x cos x, 2 cos cosy = cos@y) cos@+y) a; cos sin x + cos c, sin a; dc = sin 2x 3 sin2 = 6 2 2x2-1 8 1 4 4 Suppose instead that the system's initial state is 0) [+1 (x) + 2+3@)] // VS. Ar- gue, without performing a detailed calculation, that in this case @) does not change with time.