The following questions pertain to a harmonic oscillator. a) Use the matrix representation of the Hamiltonian...
The following questions pertain to a harmonic oscillator.
a) Use the matrix representation of the Hamiltonian operator to evaluate the expectation value <2|H|2>.
b) Use the matrix representation of the operator â to complete the following expression: â|3) = | >.
I know the answers should be
a) (a)5hν/2
B) Sqrt(3)|2
Can someone please help explain?
Homework Answers
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The following questions pertain to a harmonic oscillator.
a) Use the matrix representation of the Hamiltonian...
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could someone please help me with part c? Consider a one-dimensional harmonic oscillator, at a timet...
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4. (30 points) Harmonic oscillator with perturbation Recall the Hamiltonian of an harmonic oscillator in 1D: p21 ÃO = + mwf?, where m is the mass of the particle and w is the angular frequency. Now, let us perturb the oscillator with a quadratic potential. The perturbation is given by Î' = zgmw?h?, where g is a dimensionless constant and g <1. (a) Write down the eigen-energies of the unperturbed Hamiltonian. (b) In Lecture 3, we introduced the lowering (or...
Consider a linear harmonic oscillator whose Hamiltonian is given by 1? д2 Н 2m дд? 2 hw(n1/2) with eigenvalues En n 0,1,2,... Please (1) derive its density matrix in momentum representation, and (2) evaluate the mean energy (H with results obtained in last question
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Use ladder operator to evaluate the elements of the matrix <mixpins and <m1pxin> of a harmonic oscillator at ID And prove that mix, plln>= itdan
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could someone please help me
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Consider a one-dimensional harmonic oscillator, at a timet - 0 in the state, where In〉 is the nth energy eigenstate with energy eigenvalues En = (n + ,wo a) Write out an expression, in terms of the energies En, for the state vector at a time t. That is, write down what ^(t)) is equal to. b) Calculate the expectation value of the energy of the state vector. c) Calculate the expectation...
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