(a) Use the variational method to estimate the ground state energy of a particle of |mass...
Use the variational principle to estimate the ground state energy of a particle in the following potential: V=cx for x>0 and V=infinity for x<0 Use Dxe^-ax as your trial function and minimize as necessary with respect to a. Assume the constant c is real and greater than zero
A particle of charge q and mass m is bound in the ground state of a one-dimensional harmonic oscillator potential with frequency oo. At time t-0 a weak spatially uniform electric field (E) is turned on, so that the perturbation to the Hamiltonian can be described as R'(t) =-q Exe-t/t for t> 0. Using first order, time-dependent perturbation theory, calculate the following probabilities: (a) the particle is detected in the first excited state after a very long time (t »...
please solve with explanations 3. (20 pts) A particle of mass m and charge q is in a one dimensional harmonic oscillator potential ()1ma'. A time dependent uniform electric field E, ()E, os eris 2 applied in the x direction. The particle is in the harmonic oscillator ground state at time a) What is the time dependent perturbation Hamiltonian H'(t) - the potential enegy of the charge in this electric field? b) Find the amplitude ci(t) of finding the particle...
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.
tthe-independent Help: The operator expression dimensions is given by H 2m r ar2 [2] A particle of mass m is in a three-dimensional, spherically symmetric harmonic oscillator potential given by V(r)2r2. The particle is in the I-0 state. Noting that all eigenfunetions must be finite everywhere, find the ground-state radial wave-function R() and the ground-state energy. You do not have to nor oscillator is g (x) = C x exp(-8x2), where C and B are constants) harmonic malize the solution....
As a result of a sudden perturbation of the harmonic oscillator originally in the ground state, the restoring force coefficient k in its potential energy U(a) (1/2)k2 changes to k' ak, a>0. Find the proba- bility to find the new oscillator in an excited state. As a result of a sudden perturbation of the harmonic oscillator originally in the ground state, the restoring force coefficient k in its potential energy U(a) (1/2)k2 changes to k' ak, a>0. Find the proba-...
Suppose a particle is in a one-dimensional harmonic oscillator potential. Suppose that a perturbation is added at time t = 0 of the form . Assume that at time t = 0 the particle is in the ground state. Use first order perturbation theory to find the probability that at some time t1 > 0 the particle is in the first excited state of the harmonic oscillator. H' = ext.
1. Variational method In this problem, you will approximate the ground state wave function of a quantum system using the variational theory. Use the trial wave function below 2 cos/T) , 1x1 trial a/2 to approximate the ground state of a harmonic oscillator given by 2.2 2 using a as an adjustable parameter. (a) Calculate the expectation value for the kinetic energy, (?) trial 4 points (b) Calculate the expectation value for the potential energy, Virial. Sketch ??tria, (V)trial, and...
a) Use the variational method to estimate the binding energy of a deuteron. Assume that the potential between the proton and neutron is V(r) = Ae-r/ro where A and ro are constants and use as a trial function W(r) = Ce-Br (4) where C is the normalization constant. b) Consider the Hamiltonian of a nonharmonic oscillator d2 (5) H + x2 + x4 dx2 Use the WKB approximation to find the ground state of the system as x .
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...