In terms of 
and 
, what is the probability
at time t of measuring the particle described by this wave function
in a state of energy (Hamiltonian) E? Explain in words why
this quantity is time independent. For simplicity, in this problem
you may assume that 
is a monotonic function of 
so
that is an invertible function and the usual change of
integration variables works.
Hint: First, change
integration variables in (1) from 
to dE.