Answered: Find the locations where the… | bartleby

Related questions

Question

Find the locations where the probability density has
its maximum values for the wave function w(x) =
A(2ax² - 1)e-ax2/2, which represents the second excited
state of the simple harmonic oscillator.
I

Expert Solution

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Calculate the uncertainties dr = V(x2) and op = V(p²) for %3D a particle confined in the region -a a, r<-a. %3D
At time t = 0 a particle is described by the one-dimensional wave function 1/4 (a,0) = (²ª) e-ikre-ar² where k and a are real positive constants. Verify that the wave function (r, 0) is normalised. Hint: you may find the following standard integral useful: Loze -2² dx = √,
3. A system of N harmonic oscillators of frequency w are prepared in identical initial states of wavefunction Þ(x,0). It is found that the measurement of the energy of the system at t = 0 gives 0.5hw with probability 0.25, 1.5hw with probability 0.5 and 2.5hw with probability 0.25. a. Write a possible function p(x, 0). b. Write the corresponding (x, t). c. What is the expectation value of the Hamiltonian in the state p(x,t) ? d. Calculate the expectation value of position at time t
Answer all these questions
the ground state wavefunction of a quantum mechanical simple harmonic oscillator of mass m and frequency, which is given by: Question mw where a = the potential is V(x) = mw²x² and N is given by: N =) 9 ax² ¡Ent Yo (x, t) = Ne ze By substituting into the time-dependent Schrödinger equation, prove that the ground state energy, Eo, is given by: Eo ħw 2