Question

(a) Write out the Time Independent Schrödinger Equation (TISE) in 1D, define your terms. (b) For a time independent potential, describe how we find the solutions to the Time Dependent Schrödinger Equation (TDSE) ?(x, t) if we know the solutions to the TISE ?(x).

          (a) Write out the Time Independent Schrödinger Equation (TISE) in 1D, define your terms.
(b) For a time independent potential, describe how we find the solutions to the Time Dependent Schrödinger Equation (TDSE) ?(x, t) if we know the solutions to the TISE ?(x).

(a) Write out the Time Independent Schrödinger Equation (TISE) in 1D, define your terms.
(b) For a time independent potential, describe how we find the solutions to the Time Dependent Schrödinger Equation (TDSE) ?(x, t) if we know the solutions to the TISE ?(x).

Added by Alexis C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Kirsty Gledhill

05/26/2022

Step 1

The TDSE is given by: iħ * ∂ψ/∂t = -ħ²/2m * ∂²ψ/∂x² + V(x)ψ We can solve this equation by assuming a solution of the form ψ(x,t) = ψ(x) * T(t), where ψ(x) is the solution to the TISE and T(t) is a time-dependent part. By substitifying this into the TDSE, we Show more…

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(a) Write out the Time Independent Schrödinger Equation (TISE) in 1D, define your terms. (b) For a time independent potential, describe how we find the solutions to the Time Dependent Schrödinger Equation (TDSE) Ψ(x, t) if we know the solutions to the TISE Φ(x).