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.

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genius_generous answered 2 years ago

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

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

Method A: Based on the frequency of a simple harmonic oscillator. The angular frequency of a mass on a spring is given by ω=(k/m)1/2ω=(k/m)1/2 where m is the mass and k is the spring constant. The period of a harmonic oscillator is T=2π/ωT=2π/ω . If you do a little math, you can get a formula for the spring constant in terms of the mass and the period. a) Design a procedure to measure the spring constant based on Method A...

For the ground state of the Harmonic Oscillator and 2D Rigid Rotor A. Give the time...

For the ground state of the Harmonic Oscillator and 2D Rigid Rotor A. Give the time dependent wave function B. Determine <x> and <p> for both the Harmonic Oscillator and 2D Rigid Rotor

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 by a graphical presentation that the angular momentum is quantized, sketch.

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.

With the sun at the origin, compute the total angular momentum of the earth, and compare...

With the sun at the origin, compute the total angular momentum of the earth, and compare the magnitude of the contributions from the angular momentum of the center of mass and the angular momentum about the center of mass. You can make simplifying assumptions, like that the orbit is circular, that the earth is perfect sphere, etc.

The deuteron is a bound state of a proton and a neutron of total angular momentum...

The deuteron is a bound state of a proton and a neutron of total angular momentum j = 1. It is known to be principally an S(ℓ = 0) state with a small admixture of a D(ℓ = 2) state. Calculate the magnetic moment of the pure d state n-p system with j = 1. Assume that the n and p spins are to be coupled to make the total spin s which is then coupled to the orbital angular...

Superposition of N harmonic oscillator waves of equal amplitude equal angular frequency ω and constant incremental...

Superposition of N harmonic oscillator waves of equal amplitude equal angular frequency ω and constant incremental phase difference φ. And constant spacing d between them. The total length of the array of the oscillator is L. With L = N*d The amplitude is: where A0 the amplitude of each wave. A = A0 sin(Nφ /2) / sin(φ /2) The intensity : I = I0*(sin(Nφ /2) / sin(φ /2))^2 1. show the minimum is at Nd*sin(θ ) = m λ, m...

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.

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