Demonstrate that the WKB approximation yields the energy levels of the linear harmonic oscillator and compute...

Demonstrate that the WKB approximation yields the energy levels of the linear harmonic oscillator and compute the WKB approximation for the energy eigenfunctions for the n=0 and n=1 state and compute with the exact stationary state solutions.

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genius_generous answered 1 year ago

As in the figure below, a simple harmonic oscillator is attached to a rope of linear...

As in the figure below, a simple harmonic oscillator is attached to a rope of linear mass density 5.4 ✕ 10−2 kg/m, creating a standing transverse wave. There is a 3.5-kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 44.1 rad/s and an amplitude of 255.0 cm. (a) What is the distance between adjacent nodes? m (b) If the angular frequency of the oscillator doubles, what happens to the...

Show that the total energy of a harmonic oscillator in the absence of friction is conserved.

Quantum Mechanics Determine the settlement approach (approximation) for the harmonic oscillator system due to the relativistic...

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1. (a) Describe in your own words and mathematically the harmonic oscillator approximation to molecular vibration....

1. (a) Describe in your own words and mathematically the harmonic oscillator approximation to molecular vibration. (b) What does this approximation lack in terms of representing real molecular bonds? (c) When is the approximation most valid and when are higher order approximations necessary?

Take an eigenfunction for the harmonic oscillator and the corresponding energy eigenvalue, and substitute them into...

Take an eigenfunction for the harmonic oscillator and the corresponding energy eigenvalue, and substitute them into the Schrodinger equation. Then prove that the equation is satisfied. Do this for n =4, show how n is substituted.

The simple harmonic oscillator (SHO) is probably the single most important approximation for describing small displacements...

The simple harmonic oscillator (SHO) is probably the single most important approximation for describing small displacements about stable equilibrium positions. Why is it that the SHO approximation actually works? What are the limitations of the SHO?

Show that, in a symmetrical 2D linear harmonic oscillator, the expectation value for total angular momentum...

Show that, in a symmetrical 2D linear harmonic oscillator, the expectation value for total angular momentum is conserved with time.

1) a) Establish schrodinger equation,for a linear harmonic oscillator and solve it to obtain its eigen...

1) a) Establish schrodinger equation,for a linear harmonic oscillator and solve it to obtain its eigen values and eigen functions. b) calculate the probability of finding a simple harmonic oscillator within the classical limits if the oscillator in its normal state.

1. A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation...

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Demonstrate that the ground-state wave function for the one-dimensional harmonic oscillator satisfies the appropriate Schrodinger's equation

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