Answered: 10. Sketch the first four wavefunctions… | bartleby

Related questions

Question

10. Sketch the first four wavefunctions (n = 1 through n = 4) for the particle in a box, and sketch the
probability densities for the same wavefunctions. Can you determine (x) for these wavefunctions
without evaluating any integrals? Explain. Is this the same as the most likely location(s) for the particle,
in each case?

Expert Solution

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

There is an electron, in a 1-d, infinitely deep square potential well with a width of d. If it is in ground state, 1. Draw the electron's wavefunction. Show the position of the walls of the potential well. 2. Explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.
Consider a particle in a one-dimensional rigid box of length a. Recall that a rigid box has U (x) = 00 for x a, and U () = 0 for 0 )
Question A2 Consider an infinite square well of width L, with V = 0 in the region -L/2 < x < L/2 and V → ∞ everywhere else. For this system: a) Write down and solve the time-independent Schrödinger equation for & inside the well, where -L/2< x
1.The odd parity eigenstates of the infinte square well , with potential V = 0 in the range −L/2 ≤ ? ≤ L/2, are given by : (see figure) and have Ψn(x, t) = 0 elsewhere , for n=2 , 4 , 6 etc a) Sketch the potential of this system , including in your sketch the positions of the lowest three energy levels . Indicate in your sketch the form of the wavefunction for a particle in each of these energy levels , and state which of the wavefunctions you have drawn could be decirbed by the Ψn written above (see figure) . b) Calculate the expectation value of momentum , ⟨p⟩ for a particle with n=2 c) Calculate the expectation value of momentum squared ⟨p 2⟩ , for a particle with n = 2 . Hint : you may use the mathematical identiy sin2 x = 1/2 (1 − cos 2x) without proof .