Find <x^4> , <p^4> , for the nth stationary state of the harmonic oscillator, using the...

Find <x^4> , <p^4> , for the nth stationary state of the harmonic oscillator, using the method of example 2.5.

Example 2.5 : Find the expectation value of the potential energy in the nth state of the harmonic oscillator.

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genius_generous answered 2 years ago

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

1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for...

1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for this question and the following, you should rely heavily on the raising and lowering operators. Do not do integrals.) (a) What is the expectation value of position for this particle? (b) What is the expectation value of momentum for this particle? (c) What is ∆x for this particle? 2) Consider a harmonic oscillator potential. (a) If the particle is in the state |ψ1> =...

The motion of an harmonic oscillator is governed by the differential equation 2¨x + 3 ˙x...

The motion of an harmonic oscillator is governed by the differential equation 2¨x + 3 ˙x + 4x = g(t). i. Suppose the oscillator is unforced and the motion is started from rest with an initial displacement of 5 positive units from the equilibrium position. Will the oscillator pass through the equilibrium position multiple times? Justify your answer. ii. Now suppose the oscillator experiences a forcing function 2e t for the first two seconds, after which it is removed. Later,...

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

A harmonic oscillator is in the ground state when the parameter k DOUBLES without changing the...

A harmonic oscillator is in the ground state when the parameter k DOUBLES without changing the wavefunction. What's the probability that the oscillator is found in the new ground state?

X∼(μ=4.5,σ=4) find P(X<10.2) X∼(μ=4.5,σ=4) find P(X>-2.8) For X∼(μ=4.5,σ=4) find P(6.7<X<15.9) For X∼(μ=4.5,σ=4) find P(-4.9<X<-0.2) For X∼(μ=4.4,σ=4)...

X∼(μ=4.5,σ=4) find P(X<10.2) X∼(μ=4.5,σ=4) find P(X>-2.8) For X∼(μ=4.5,σ=4) find P(6.7<X<15.9) For X∼(μ=4.5,σ=4) find P(-4.9<X<-0.2) For X∼(μ=4.4,σ=4) find the 2-th percentile. For X∼(μ=17.4,σ=2.9) find the 82-th percentile. For X∼(μ=48.1,σ=3.4) find the 13-th percentile. For X∼(μ=17.4,σ=2.9) find the 49-th percentile. For X∼(μ=48.1,σ=3.4) find P(X>39) For X∼(μ=48.1,σ=3.4) find P(X<39)

The Simple harmonic oscillator: A particle of mass m constrained to move in the x-direction only...

The Simple harmonic oscillator: A particle of mass m constrained to move in the x-direction only is subject to a force F(x) = −kx, where k is a constant. Show that the equation of motion can be written in the form d^2x/dt2 + ω^2ox = 0, where ω^2o = k/m . (a) Show by direct substitution that the expression x = A cos ω0t + B sin ω0t where A and B are constants, is a solution and explain the...

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Find <x^4> , <p^4> , for the nth stationary state of the harmonic oscillator, using the...

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