Question

Show that ?(x) = B × e^(-½ m?/? x²) satisfies the single harmonic oscillator Schrödinger equation, where ? = ?(k/m), k is the spring constant and m the particle mass. (a) What is the energy of the state given by this wavefunction? (Mathemati- cally speaking, this wavefunction solves the eigenvalue problem ?? = E? for E.) (b) What is the potential energy of this state? What is the kinetic energy of this state?

          Show that
?(x) = B × e^(-½ m?/? x²)
satisfies the single harmonic oscillator Schrödinger equation, where ? = ?(k/m),
k is the spring constant and m the particle mass.

(a) What is the energy of the state given by this wavefunction? (Mathemati-
cally speaking, this wavefunction solves the eigenvalue problem ?? = E?
for E.)
(b) What is the potential energy of this state? What is the kinetic energy of
this state?

Show that
?(x) = B × e^(-½ m?/? x²)
satisfies the single harmonic oscillator Schrödinger equation, where ? = ?(k/m),
k is the spring constant and m the particle mass.

(a) What is the energy of the state given by this wavefunction? (Mathemati-
cally speaking, this wavefunction solves the eigenvalue problem ?? = E?
for E.)
(b) What is the potential energy of this state? What is the kinetic energy of
this state?

Added by Aitor H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Madhur L

05/04/2022

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Show that Έ(x) = B x e^(-1/2 mω/ℏ x^2) satisfies the single harmonic oscillator Schrödinger equation, where ω = √(k/m), k is the spring constant and m the particle mass. (a) What is the energy of the state given by this wavefunction? (Mathematically speaking, this wavefunction solves the eigenvalue problem Ĥψ = Eψ for E.) (b) What is the potential energy of this state? What is the kinetic energy of this state?