Answered: The time-independent wave function of a… | bartleby

Related questions

Question

The time-independent wave function of a particle of mass m moving in a potential V =dx
is
ma?
a being a constant.
Find the energy of the system.

The time-independent wave function of a particle of mass m moving in a potential V(x) = ad*
%3D
is
ma
y(x) = exp
a being a constant.
Find the energy of the system.

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

5. Consider a potential barrier represented as follows: U M 0 +a U(x) = x a Determine the transmission coefficient as a function of particle energy.
A 4.90g Particle confined to a box of length L has a speed of 4.70mm/s a) lalhat is the classical Kinetic energy of Particle? the b) If the energy of the first excited State (n=2) is equal to the Kinetic energy found in part (a), what is the value Note: Answer must be in mi L? of c) Is the result found in part (b) realistic ? Explain.
Consider the wavefunction Y(x) = exp(-2a|x|). a) Normalize the above wavefunction. b) Sketch the probability density of the above wavefunction. c) What is the probability of finding the particle in the range 0 < x s 1/a ?
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.
Consider the one-dimensional step-potential V (x) = {0 , x < 0; V0 , x > 0}(a) Calculate the probability R that an incoming particle propagating from the x < 0 region to the right will reflect from the step.(b) Calculate the probability T that the particle will be transmitted across the step.(c) Discuss the dependence of R and T on the energy E of the particle, and show that always R+T = 1.[Hints: Use the expression J = (-i*hbar / 2m)*(ψ*(x)ψ′(x) − ψ*'(x)ψ(x)) for the particle current to define current carried by the incoming wave Ji, reflected wave Jr, and transmitted wave Jt across the step.For a simple plane wave ψ(x) = eikx, the current J = hbar*k/m = p/m = v equals the classical particle velocity v. The reflection probability is R = |Jr/Ji|, and the transmission probability is T = |Jt/Ji|. You need to write and solve the Schrodinger equation in regions x < 0 and x > 0 separately, and connect the solutions via boundary conditions at x = 0 (ψ(x) and ψ′(x) must be…
(d) Prove that for a classical particle moving from left to right in a box with constant speed v, the average position = (1/T) ff x(t) dt = L/2, where T L/v is the time taken to move from left to right. And = : (1/T) S²x² (t) dt L²/3. Hint: Only consider a particle moving from left x = 0 to right x = L = and do not include the bouncing motion from right to left. The results for left to right are independent of the sense of motion and therefore the same results apply to all the bounces, so that we can prove it for just one sense of motion. Thus, the classical result is obtained from the Quantum solution when n >> 1. That is, for large energies compared to the minimum energy of the wave-particle system. This is usually referred to as the Classical Limit for Large Quantum Numbers.