Question

In: Physics

Consider the asymmetric 1/2 harmonic oscillator. use the Variational Principle to estimate the ground state energy...

Consider the asymmetric 1/2 harmonic oscillator. use the Variational Principle to estimate the ground state energy of this potential. Use as your trial function Axe^bx^2

Solutions

Expert Solution


Related Solutions

Consider a system composed of four harmonic oscillators. The energy of the ground state is E0/2....
Consider a system composed of four harmonic oscillators. The energy of the ground state is E0/2. The distribution of oscillators in each system is described by the set following distributions {Ni}  Distribution I: N0=2, N1=1 N2=1, N3=0  Distribution II: N0=1, N1=3 N2=N3=0  Distribution III: N0=3 N1=N2=0 N3=1 For each distribution, calculate. 1. The energy of each system and the average energy 2. The number of equivalent particle arrangements W that yield equivalent distributions (assume the particles are...
For the ground state of the Harmonic Oscillator and 2D Rigid Rotor A. Give the time...
For the ground state of the Harmonic Oscillator and 2D Rigid Rotor A. Give the time dependent wave function B. Determine <x> and <p> for both the Harmonic Oscillator and 2D Rigid Rotor
A harmonic oscillator is in the ground state when the parameter k DOUBLES without changing the...
A harmonic oscillator is in the ground state when the parameter k DOUBLES without changing the wavefunction. What's the probability that the oscillator is found in the new ground state?
1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for...
1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for this question and the following, you should rely heavily on the raising and lowering operators. Do not do integrals.) (a) What is the expectation value of position for this particle? (b) What is the expectation value of momentum for this particle? (c) What is ∆x for this particle? 2) Consider a harmonic oscillator potential. (a) If the particle is in the state |ψ1> =...
Use the Heisenberg uncertainty principle to explain why does the harmonic oscillator have a zero point...
Use the Heisenberg uncertainty principle to explain why does the harmonic oscillator have a zero point energy, but the rigid rotor does not?
In the harmonic oscillator problem, the normalized wave functions for the ground and first excited states...
In the harmonic oscillator problem, the normalized wave functions for the ground and first excited states are ψ0 and ψ1. Using these functions, at some point t, a wave function u = Aψ0 + Bψ1 is constructed, where A and B are real numbers. (a) Show that the average value of x in the u state is generally non-zero. (b) What condition A and B must satisfy if we want the function u to be normalized? (c) For which values...
Show that the total energy of a harmonic oscillator in the absence of friction is conserved.
Show that the total energy of a harmonic oscillator in the absence of friction is conserved.
Consider the ground state energy of the hydrogen atom E0. Enter the expression you use to...
Consider the ground state energy of the hydrogen atom E0. Enter the expression you use to verify that the ground state energy is 13.6 eV? Use fundamental constants e, me, k and h. E0 = ?
1. Consider an electron in a 1D harmonic oscillator potential. Suppose the electron is in a...
1. Consider an electron in a 1D harmonic oscillator potential. Suppose the electron is in a state which is an equal mix of the ground state and the first-excited state. a) Write the time-dependent state in Dirac notation. b) Calculate 〈x〉. Calculate 〈p〉 using raising and lower operators. c) Graph 〈x〉 as a function of time.
1. A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation...
1. A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation amplitude is 20.0cm. what is the oscillation frequency? 2. A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring? 3. An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field. The...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT