5 Questions
What is the Hamiltonian operator of the harmonic oscillator in one dimension?
Ĥ = p̂2 1 + mω 2 x̂2 / 2m
What does the eigenvalue equation for the harmonic oscillator look like in the {|xi} representation?
− ~2 d2ϕ(x)/dx2 + mωxϕ(x) = Eϕ(x)
What can be deduced about the eigenvalues of the Hamiltonian from the form of the potential function?
The eigenvalues of the Hamiltonian are positive.
What happens to the eigenvalues E of the Hamiltonian if the potential function V (x) is greater than its minimum value Vm?
The eigenvalues E are greater than Vm.
What kind of system is described by the Hamiltonian operator for the harmonic oscillator?
Time-independent (conservative system)
Dive into the study of the quantum harmonic oscillator, an essential quantum system. Explore the eigenvalues, creation and annihilation operators, and spectrum determination.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
