a) Write down the one-dimensional time-dependent Schro ̈dinger equation for a particle of mass m described by a wavefunction Ψ(t, x) in a potential V (x). b) For energy eigenstates, the wavefunction can be written as Ψ(t, x) = f (t) ψ(x). For this wavefunction: (i) state the time-independent equation that must be satisfied by ψ(x). (ii) derive an expression for f(t), in terms of the energy of the particle E.
a) Write down the one-dimensional time-dependent Schro ̈dinger equation for a particle of mass m described by a wavefunction Ψ(t, x) in a potential V (x). b) For energy eigenstates, the wavefunction can be written as Ψ(t, x) = f (t) ψ(x). For this wavefunction: (i) state the time-independent equation that must be satisfied by ψ(x). (ii) derive an expression for f(t), in terms of the energy of the particle E.
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a) Write down the one-dimensional time-dependent Schro ̈dinger equation for a particle of
mass m described by a wavefunction Ψ(t, x) in a potential V (x). b) For energy eigenstates, the wavefunction can be written as
Ψ(t, x) = f (t) ψ(x).
For this wavefunction:
(i) state the time-independent equation that must be satisfied by ψ(x).
(ii) derive an expression for f(t), in terms of the energy of the particle E.
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