Answered: PROBLEM 1 Consider a ld oscillator… | bartleby

Related questions

Question

PROBLEM 1 Consider a 1d oscillator subject to an additional constant force
F, so that the potential energy is given by:
mw?
-x² – Fx
2
U (x) =
|
Using the solution of the SE for oscillator at F = 0, write down the wave
functions and the energy levels at F > 0. Can the ground state energy of
ocillator under a constant force be negative?
HINT: The force F causes a displacement of U(x) without changing its
parabolic shape.

Expert Solution

Step 1

Wavefunction obtained for a normal harmonic oscillator is,

$ψ_{n} (x) = \frac{1}{\sqrt{2^{n} n!}} {(\frac{m ω}{π ℏ})}^{\frac{1}{4}} e^{- \frac{m ω x^{2}}{2 ℏ}} H_{n} (\sqrt{\frac{m ω}{ℏ}} x)$

Energy is,

$E_{n} = (n + \frac{1}{2}) ℏ ω$

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

qx = exp(-ßhv) 1-exp(-ßhv) Derive the partition function for a single harmonic oscillator in three different directions. Briefly note any assumptions made
Solve the following.
A proton is confined in box whose width is d = 750 nm. It is in the n = 3 energy state. What is the probability that the proton will be found within a distance of d/n from one of the walls? Include a sketch of U(x) and ?(x). Sketch the situation, defining all your variables
PROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground state (n = 0). Calculate the mean square dispersions (x2), (p²), and the product (r2)(p²).
1
For the potential-energy functions shown below, spanning width L, can a particle on the left side of the potential well (x 0.55L)? If not, why not? b. c. 0 a. 0o 00 E E E-
Consider a finite potential step with V = V0 in the region x < 0, and V = 0 in the region x > 0 (image). For particles with energy E > V0, and coming into the system from the left, what would be the wavefunction used to describe the “transmitted” particles and the wavefunction used to describe the “reflected” particles?
Consider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy U(x) = 00 for a O where k is the spring constant. What are the energies of the ground state and fırst excited state? Explain your reasoning. Give the energies in terms of the oscillator frequency wo = Vk/m. Formulas.pdf (Click here-->)