From A Modern Approach to Quantum Mechanics by Townsend
From A Modern Approach to Quantum Mechanics by Townsend 12.6. Consider the one-dimensional system of a...
Introduction to Quantum Mechanics problem: 3. Find the normalized stationary states and allowed bound state energies of the Schrodinger equation for a particle of mass m and energy E < Vo in the semi-infinite potential well Vo 0.
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...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
Consider a one-dimensional well with one impenetrable wall. The potential energy is given by 0 x < 0 V(x) = { -V. 0 < x < a 10 x > a We showed in the homework that the allowed energies for the eigenstates of a bound particle (E < 0) in this potential well satisfy the transcendental function -cotĚ = 16 - 52 $2 where 5 = koa, and ko = V2m(Vo + E)/ħ, and 5o = av2mV /ħ (a)...
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...
quantum mechanics Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2 Consider a particle confined in two-dimensional box with infinite...
Quantum Mechanics II, 'Quantum Mechanics', David H. McIntyre 3. Consider two identical linear oscillators with spring constant k. The Hamiltonian is ha d k (2 + x) H 1 + + 122, 2m d. 2 where x1 and 22 are oscillator variable. (a) by changing the variables 11 = x +, 19=xY find the energies of the three lowest states of this system? (b) If the particle are with spin 1/2, which of the above three states are triplet states...
Consider a particle in a 1-dimensional ininite square well potential {0, V(z)=Í oo, (-a < z <a) elsewhere The particle is initially localized in the right side of the well (O S a) Calculate the probability that at later times, an energy measurement will yield the energy of the first excited state of this system
This question assesses the gravitational attraction due to a cylinder of mass. Consider a cylinder with radius R equal to the mean radius of the Earth, length L and a mass M equal to the mass of the Earth. The specific task is to determine the escape velocity from the end of the cylinder. First, though, consider a different but related problem: a particle with mass mp placed a distance r from the center of a ring of mass M,...
Quantum Mechanics Problem 1. (25) Consider an infinite potential well with the following shape: 0 a/4 3al4 a h2 where 4 Using the ground state wavefunction of the original infinite potential well as a trial function, 2πχ trial = 1-sin- find the approximation of the ground state energy for this system with the variational method. (Note, this question is simplified by considering the two components of the Hamiltonian, and V, on their own) b) If we had used the 1st...