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please help me with problem quantum mechanis
please please help me with problem quantum mechanis e haue a one-dimensional harmonic oscllo or a disturbonce o 5u b...
Quantum Mechanics
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6.- Let a and at the annihilation and creation operators for the one-dimensional harmonic oscillator and let v and w be constants. Determine the Hamiltonian eigenvalues spectrum. Î = ħwata +v(at +a)
QUANTUM MECHANICS
Problem 4 Consider a one-dimensional charged harmonic oscillator. Let the coordinate be, charge be q, mass be m, and the frequency of the oscillator be u. (a) 79 rat t =-oo, the oscillator is in the ground state 10). A uniform electric field E along x axis is applied betweentoo andtoo with the time dependence of E being given by E(t) ー(t/ア Neglect the induced magnetic field. Find the probability that the oscillator goes to the nth excited...
Quantum Mechanics
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2. An important problem of quantum mechanics is that of the particle subject to a linear res- titutive force (harmonic oscillator). The stationary Schrödinger equation for this problem, in one dimension, has the form h² #20 Ika-6 = EⓇ 2m 8x2 + 2k2O = Eº where k is the oscillator constant. Solutions of the following types are proposed: a) 6...
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Consider a one-dimensional harmonic oscillator, at a timet - 0 in the state, where In〉 is the nth energy eigenstate with energy eigenvalues En = (n + ,wo a) Write out an expression, in terms of the energies En, for the state vector at a time t. That is, write down what ^(t)) is equal to. b) Calculate the expectation value of the energy of the state vector. c) Calculate the expectation...
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Q1. Consider a particle of mass m moving in a one-dimensional harmonic oscillator potential. 1. Calculate the product of uncertainties in position and momentum for the particle in 2. Compare the result of (a) with the uncertainty product when the particle is in its the fifth excited state, ie. (OxơP)5. lowest energy state.
Q1. Consider a particle of mass m moving in a one-dimensional...
Find the Chemical Potential of the one dimensional and two dimensional harmonic oscillator. Please show all work. Thanks!
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Problem 30: 2D harmonic Oscillator (6 pts Setup the Hamilton-Jacobi Differntial equation in cartesian coordinates for the 2-dimensional harmonic oscillator and solve it. Find x(t) and y(t)
Problem 30: 2D harmonic Oscillator (6 pts Setup the Hamilton-Jacobi Differntial equation in cartesian coordinates for the 2-dimensional harmonic oscillator and solve it. Find x(t) and y(t)
1. Consider a one-dimensional simple harmonic oscillator. We know that the total energy (E) has values: Here the angular frequency (o) corresponds to the freshman physics value of [spring constant/massja and (n) can be 0, 1,2, any non-negative integer. We know that the total energy is a measurable, observable quantity. The total energy includes the kinetic energy and the potential energy. Please explain whether or not the kinetic energy and the potential energy can both be measured at the same...
In class we solved the quantum harmonic oscillator problem for a diatomic molecule. As part of that solution we transformed coordinates from x, the oscillator displacement coordinate, to the unitless, y using the relationship where μ is the reduced mass of the diatomic molecule and k is the force constant. The solutions turned out to be: w(y)N,H, (y)e Where N is a normalization constant, H,(v) are the Hermit polynomials and v is the quantum number with values of v0,1,2,3,.. The...
Quantum Mechanics. Consider a one-dimensional harmonic oscillator of frequency found in the ground state. At a perturbation is activated. Obtain an expression for the expected value of as a function of time using time-dependent perturbation theory. A step by step process is deeply appreciated. The best handwriting possible, please. Thank you very much. We were unable to transcribe this imageWe were unable to transcribe this imageV (t) = Fox cos (at) We were unable to transcribe this image V (t)...