Answered: a) Write down an expression for the… | bartleby

Related questions

Question

a) Write down an expression for the probability density ρ(t, x) of a particle described by the

wavefunction Ψ(t, x).
b) Using the probability density, explain how you would calculate the probability of finding this

particle in the interval between x = A and x = B.

Expert Solution

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

a) Write down the one-dimensional time-dependent Schro ̈dinger equation for a wavefunction Ψ(t, x) in a potential V (x). b) Write down the one-dimensional time-independent Schro ̈dinger equation for a wavefunc- tion ψ(x) in a potential V (x). c) Assuming that Ψ(t,x) corresponds to an energy eigenstate, write down a mathematical expression that relates the solutions of the one-dimensional time-dependent and time- independentSchro ̈dingerequations,Ψ(t,x)andψ(x).
Show that the probability associated with the state Ψn for a particle in a one- dimensional box 0≤ x≤ L obeys the following relationship: (You can see the picture attached for the problem)
WHY DOES THE WAVE- FUNCTION GO TO ZERO AS X GOES TO * INFINITY ?
a question of quantum mechanics: Consider a particle in a two-dimensional potential as shown in the picture Suppose the particle is in the ground state. If we measure the position of the particle, what isthe probability of detecting it in region 0<=x,y<=L/2 ?
Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).
A particle is described by the wavefunction Ψ(t, x), and the momentum operator is denoted by pˆ. a) Write down an expression for the differential operator pˆ. b) Write down an expression for the expectation value of the momentum, ⟨p⟩. c) Write down an expression for the probability density, ρ. d) Write down an expression for the probability of finding the particle between x = a and x = b.
3
B7
(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.