Question

Starting from the Schrödinger equation in Dirac notation for a time independent Hamiltonian ( H ), [ i hbar frac{d}{d t}|psi(t) angle=H|psi(t) angle, ] show that the solutions projected onto a position basis take the form, [ Psi(vec{r}, t)=exp [-i E t / hbar] psi(vec{r}) . ] State why the energy eigenvalues are real.

          Starting from the Schrödinger equation in Dirac notation for a time independent Hamiltonian ( H ),
[
i hbar frac{d}{d t}|psi(t)
angle=H|psi(t)
angle,
]
show that the solutions projected onto a position basis take the form,
[
Psi(vec{r}, t)=exp [-i E t / hbar] psi(vec{r}) .
]
State why the energy eigenvalues are real.

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$Starting from the Schrödinger equation in Dirac notation for a time independent Hamiltonian ( H ), [ i hbar fracdd t|psi(t) angle=H|psi(t) angle, ] show that the solutions projected onto a position basis take the form, [ Psi(vecr, t)=exp [-i E t / hbar] psi(vecr) . ] State why the energy eigenvalues are real.$

Added by Foster J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Frank Deng

05/09/2022

Step 1

Step 1: Start with the Schrödinger equation in Dirac notation for a time-independent Hamiltonian H: \(i\hbar \frac{d}{dt}|\psi(t)\rangle = H|\psi(t)\rangle\). Show more…

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Starting from the Schrödinger equation in Dirac notation for a time independent Hamiltonian H, iℏ d/dt|ψ(t)⟩ = H|ψ(t)⟩, show that the solutions projected onto a position basis take the form, Ψ(r⃗, t) = exp[−iEt/ℏ]ψ(r⃗). State why the energy eigenvalues are real.

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