SOLVED:A particle in the infinite square well has as its initial wave function an even mixture of the first two stationary states: Ψ(x, 0)=A[ψ1(x) ψ2(x)]. (a) Normalize Ψ(x, 0). (That is, find A. This is very easy, if you exploit the orthonormality of ψ1 and ψ2 . Recall that, having normalized Ψat t=0 you can rest assured that it stays normalized- if you doubt this, check it explicitly after doing part (b).) (b) Find Ψ(x, t) and |Ψ(x, t)|^2 . Express the latter as a sinusoidal function of time,
SOLVED:A particle in the infinite square well has as its initial wave fun…
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The case of an infinite square well whose right wall expands at a constant velocity (v) can be solved exactly. A complete set of solutions is Φn(x, t) ≡√((2)/(w)) sin((n π)/(w) x) e^.i m v x^2-2 En^' a t) / 2 ħv where w(t) ≡a v t is the width of the well and En^i ≡n^2 π^2 ħ^2 / 2 m a^2 is the n th allowed | Numerade
The case of an infinite square well whose right wall expands at a consta…
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