Question: physical chem question. please answer Harmonic Oscillator Question and Answer 1. Write the complete Schroedinger equation of an one-dimensional harmonic oscillator, Define all the terms.

physical chem question. please answer

Harmonic Oscillator Question and Answer 1. Write the complete Schroedinger equation of an one-dimensional harmonic oscillator, Define all the terms. 2. The ground state wave function (un-normalized) of the harmonic oscillator is 0=e22=()1/2 q=xxeq,q is the displacement, x= bond length, xeq= equilibrium bond length. (a) Normalize the wave function. (b) Find the average displacement in the ground state, that is determine q. 3. From the ground state of Q.2, find the first excited state of a harmonic oscillator by applying creation operator. Make sure to normalize the wave function, if it was not normalized. 4. Find the average displacement and the average bond length of a harmonic oscillator in its 1st excited state. 5. From the 1st excited state of Q.3, find the 2nd excited state of a harmonic oscillator by applying creation operator. Make sure to normalize the wave function if it was not normalized. 6. Find the average displacement and the average bond length of a harmonic oscillator in its 2nd excited state

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