Time-dependent Schrodinger equation is of the form
a = A4
Where a is a constant.
Show that this equation has the following property. Let H be the Hamiltonian of
a system composed of two independent parts, so that
A(x1,x2) = A1 (x1) + A2(x2)
And let the stationary states of system 1 be 41 (x1,t) and those of system 2 be
42 (x2,t). Then the stationary states of the composite system are
4(x1,X2, t) = 41(x1,t)42(x2,t)
That is, show that this product forms a solution to the preceding equation for
the given composite Hamiltonian.
b. Show that this property is not obeyed by a wave equation that is second order in
time, such as
a2 a24 at² = A4
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