Solve the quantum harmonic oscillator problem by using the matrix method.

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genius_generous answered 2 years ago

Solve the quantum simple harmonic oscillator in three dimensions i.e. find the energy and eigenkets. It's...

Solve the quantum simple harmonic oscillator in three dimensions i.e. find the energy and eigenkets. It's solution will include hermite polynomials.

QUANTUM MECHANICS-upper level In the harmonic oscillator problem, the normalized wave functions for the ground and...

QUANTUM MECHANICS-upper level In the harmonic oscillator problem, the normalized wave functions for the ground and first excited states are ψ0 and ψ1. Using these functions, at some point t, a wave function u = Aψ0 + Bψ1 is constructed, where A and B are real numbers. (a) Show that the average value of x in the u state is generally non-zero. (b) What condition A and B must satisfy if we want the function u to be normalized? (c)...

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The solution of the Schrödinger's Equation for the quantum-mechanical harmonic oscillator includes the Hermite polynomials in the wavefunctions. (In the following questions be sure to define all symbols.) Please make sure your writing is legible (a) Write the differential equation for which the Hermite polynomials are the solution. (b) State the recursion relation for the Hermite polynomials and be sure to define all symbols. (c) Write the mathematical expression for the orthogonality of the Hermite polynomials and be sure to...

Explain why in the case of the quantum harmonic oscillator the wave function can cross the...

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Method A: Based on the frequency of a simple harmonic oscillator. The angular frequency of a...

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In the harmonic oscillator problem, the normalized wave functions for the ground and first excited states...

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Solve schroedinger's equation for a three dimensional harmonic oscillator and obtain its eigen values and eigen...

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1) What is ? for a harmonic oscillator (in terms of the period)?

1) What is ? for a harmonic oscillator (in terms of the period)? 2) What is ? for a spring? A) If you increase the amplitude, what happens to the period? B) If you increase the mass, what happens to the period? C) If you increase the spring constant, what happens to the period? 3) What is ? for a simple pendulum? A) If you increase the amplitude, what happens to the period? B) If you increase the mass,...

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