Write a matrix representation for position and momentum operators on bases made of eigenstates oscillator modes.
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- If a wavefunction is normalized at time t=0, show that it remains normalized at all times.Show the matrix representation of the operators a. position (x) b. momentum (p) for the one-dimensional harmonic oscillator problem. (Hint: Connect with operators A and At)Show that the following wave function is normalized. Remember to square it first. Limits of integration go from -infinity to infinity. DO NOT SKIP ANY STEPS IN THE PROCEDURE
- By employing the prescribed definitions of the raising and lowering operators pertaining to the one-dimensional harmonic oscillator: x = ħ 2mω -(â+ + â_) hmw ê = i Compute the expectation values of the following quantities for the nth stationary staten. Keep in mind that the stationary states form an orthogonal set. 2 · (â+ − â_) [ pm 4ndx YmVndx = 8mn a. The position of particle (x) b. The momentum of the particle (p). c. (x²) d. (p²) e. Confirm that the uncertainty principle is satisfied for all values of nwhat are canonical transformations 2 generating function F = 1 m 9² cot @. ㅗ Discuss the problem of linear harmonic oscillator. Usingwrite down the average of a plank oscillator and show the that its leads to the classical result under the condition of high temperature. (b) what is the average energy of one dimesnional classical oscillator?
- Need full detailed answer.My system is a pendulum attached to moving horizontal mass m_1 and the pendulum m_2 that is shifted by X_o from origin. I have the lagrangian of my system what would be my equations of motions in terms of small angle approximation and what’s is their frequency?Classical mechanics
- What do you Harmonic mean by ascillator. Prove that the Hamiltonian For Harmonic oscillator Can be weittenas H= Px 212 mwSuppose that an input of x(t) is applied to a causal LTI system whose magnitude response and phase response of transfer function H(w) is given below Thanksshow that the following wave function is normalized. Remember to square it first. Show full and complete procedure