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I have done all the work explicitly for better understanding , Please let me know if there is any error
Consider a 3D harmonic oscillator of mass m under the potential U(x,y,z) = m(w1?x2 + wz?y2...
Consider a particle subjected to a harmonic oscillator potential of the form x)m. The allowed values of energy for the simple harmonic oscillator is (a) What is the energy corresponding to the ground state (3 points)? (b) What is the energy separation between the ground state and the first excited state (3 points)? (c) The selection rule allows only those transitions for which the quantum number changes by 1. What is the energy of photon necessary to make the transition...
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by Knowing that the ground state of the particle at a certain instant is described by the wave function mw 1/4 _mw2 Th / calculate (for the ground state): a) The mean value of the position <x> (2 marks) b) The mean value of the position squared < x2 > (2 marks) c) the mean value of the momentum <p> (2...
Please do this problem about quantum mechanic harmonic oscillator and show all your steps thank you. 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...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy , and ф are the usual spherical coordinates. (a) In the form given above, why is it clear that the potential energy function V) is (b) For this problem, it will be more convenient to express this spherically-symmetric where r , spherically symmetric? A brief answer is sufficient. potential energy in Cartesian coordinates x, y, and z as physically the same potential energy as the...
A one-particle two-dimensional harmonic oscillator has the potential energy function V=V(x,y)=k/2(x2+y2). write the time-independent SchrÖdinger equation for the system and the energy eigenvalues. Define clearly the symbols you used.
3. Consider a particle of mass m moving in a potential given by: W (2, y, z) = 0 < x <a,0 < y <a l+o, elsewhere a) Write down the total energy and the 3D wavefunction for this particle. b) Assuming that hw > 312 h2/(2ma), find the energies and the corresponding degen- eracies for the ground state and the first excited state. c) Assume now that, in addition to the potential V(x, y, z), this particle also has...
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state and first excited state respectively. (a) Write the normalization condition for lv(o) and determine the mean value (H) of the energy in terms of co and ci. (b) With the additional requirement (H)-ho. calculate eoand o,p. [4] Consider a harmonic oscillator...
1. Consider a charged particle bound in the harmonic oscillator potential V(x) = mw x2. A weak electric field is applied to the system such that the potential energy, U(X), now has an extra term: V(x) = -qEx. We write the full Hamiltonian as H = Ho +V(x) where Ho = Px +mw x2 V(x) = –qEx. (a) Write down the unperturbed energies, EO. (b) Find the first-order correction to E . (c) Calculate the second-order correction to E ....
4- FOR a Quartun harmonic oscillator OF MASS M, Show That The FUNCTION f(x)= x ě * 2 is EIGENFUNCTION Of The Hamiltonian. Give The genualue, Alue. x= (mk) Esln+ 1 l hv 2 -- For The 37 Excited STATE of the RiGiD ROTOR calculate the energy, the Angular momentul & Lz .
9.5 A particle of mass m is in the ground state in the harmonic oscillator potential A small perturbation Bx6 is added to this potential (a) What are the units of ?? (b) How small must B be in order for perturbation theory to be valid? (c) Calculate the first-order change in the energy of the particle.