Question

2. Momentum space (a) Write down the Schrödinger equation in momentum space for a free particle, and solve it. (b) Given the initial state $phi(p, 0)$, use the Fourier transform relationship to write down the wave-function $psi(x, t)$ in position space at time $t$ [You don't need to evaluate the integral].

          2. Momentum space
(a) Write down the Schrödinger equation in momentum space for a free particle, and solve it.
(b) Given the initial state $phi(p, 0)$, use the Fourier transform relationship to write down the wave-function $psi(x, t)$ in position space at time $t$ [You don't need to evaluate the integral].

2. Momentum space
(a) Write down the Schrödinger equation in momentum space for a free particle, and solve it.
(b) Given the initial state phi(p, 0), use the Fourier transform relationship to write down the wave-function psi(x, t) in position space at time t [You don't need to evaluate the integral].

Added by Jessica S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

07/28/2023

Step 1

To solve this equation, we can use separation of variables and assume that ψ(p,t) can be written as: ψ(p,t) = e^(-iEt/ħ) φ(p) where E = p^2/2m is the energy of the particle. Substituting this into the Schrodinger equation, we get: iħ∂φ(p)/∂t = Eφ(p) which has Show more…

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2. Momentum space (a) Write down the Schrödinger equation in momentum space for a free particle, and solve it. (b) Given the initial state ϕ(p, 0), use the Fourier transform relationship to write down the wave-function ψ(x, t) in position space at time t [You don't need to evaluate the integral].