Write down the three-dimensional time-dependent Schro ̈dinger equation for a wavefunction Ψ(t, x) in a potential V (t, x). b)  State the condition that the potential must obey in order to derive the time-independent Schro ̈dinger equation from the time-dependent Schro ̈dinger equation. c)  Write down the three-dimensional time-independent Schro ̈dinger equation for a wavefunc- tion ψ(x) in a potential V (x). d)  State the mathematical relationship between the wavefunctions Ψ(t, x) and ψ(x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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  1. a)  Write down the three-dimensional time-dependent Schro ̈dinger equation for a wavefunction

    Ψ(t, x) in a potential V (t, x).

  2. b)  State the condition that the potential must obey in order to derive the time-independent

    Schro ̈dinger equation from the time-dependent Schro ̈dinger equation.

  3. c)  Write down the three-dimensional time-independent Schro ̈dinger equation for a wavefunc-

    tion ψ(x) in a potential V (x).

  4. d)  State the mathematical relationship between the wavefunctions Ψ(t, x) and ψ(x).

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