Answered: Consider a particle in the first… | bartleby

Related questions

Question

Consider a particle in the first excited state of an infinite square well of width L. This particle has
wavefunction
*60 = √ (7)
4₂(x)
sin
L
for -L/2 ≤ x ≤ L/2, and 2(x) = 0 elsewhere.
a) What is the value of the energy of this particle, E₂?
b)
What is the probability density function, p, for this particle?
c) At what values of does the probability density vanish?
d)
What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Consider a particle in a 2-D box having Lx = 10 nm and Ly = 10 nm. a) Make a surface plot of all the wave functions for the first and second energy levels. b) What is the degeneracy of the second energy level? Compare and contrast the wave functions of the second energy level. c) How does the number of nodes in the x-coordinate change as n increases? How does the number of nodes in the y-coordinate change as n, increases? d) Explain whether or not those same states would be degenerate if Lx = 10 nm and Ly = 15 nm.
A quantum system has a ground state with energy Eo = 0 meV and a 2-fold degenerate excited state with energy E₁ = 50 meV. E1 Calculate the probability of finding the system in its ground state when it is at T = 300 K. Select one: O a. 0.78 O b. 0.22 O c. 1 O d. 0.87
An electron is moving as a free particle in the -xdirection with momentum that has magnitude 4.50 * 10-24 kg,m/s. What is the one-dimensional time-dependent wave function of the electron?
A particle of mass m is moving in one-dimension in a potential V (x) with zero energy. The wave function for the particle is Þ(x) = Axe-x²/a? Where A and a are constants a) Use Schrodinger equation to find the potential energy V (x) of the particle. b) Evaluate your answer at x = 0
(x, t) = Ae-iwt e-(mw/ħ).x² which is a solution to Schrödinger's equation. Determine the potential V(x) that is consistent with this wave function, Note: You do not have to normalize V since Schrödinger's equation is linear.