Question

Normalize the following wave function (3) Ψ(x, t) = ( Ce−γx+iδt, x ≥ 0 0, x...

Normalize the following wave function (3)
Ψ(x, t) = (
Ce−γx+iδt, x ≥ 0
0, x < 0
where γ and δ are some real constants and γ > 0.

Homework Answers

Answer #1

for

for

Now the normalization condition is,

Here,

for

for

So,

So, the normalized wavefunction is,

for

for

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A free particle has the initial wave function Ψ(x, 0) = Ae−ax2 where A and a...
A free particle has the initial wave function Ψ(x, 0) = Ae−ax2 where A and a are real and positive constants. (a) Normalize it. (b) Find Ψ(x, t). (c) Find |Ψ(x, t)| 2 . Express your result in terms of the quantity w ≡ p a/ [1 + (2~at/m) 2 ]. At t = 0 plot |Ψ| 2 . Now plot |Ψ| 2 for some very large t. Qualitatively, what happens to |Ψ| 2 , as time goes on? (d)...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.33a in a small interval of width 0.01a? (c) What is the probability for the particle to be found...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are positive real constants. (a) Using the normalization condition, find b in terms of a. (b) What is the probability to find the particle at x = 0.33a in a small interval of width 0.01a? (c) What is the probability for the particle to be found...
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2) cos(πx/2) on the...
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2) cos(πx/2) on the interval 0 ≤ x ≤ 1. (1) What is the normalization constant, C? (2) Express ψ(x,0) as a linear combination of the eigenstates of the infinite square well on the interval, 0 < x < 1. (You will only need two terms.) (3) The energies of the eigenstates are En = h̄2π2n2/(2m) for a = 1. What is ψ(x, t)? (4) Compute the expectation...
Consider the following wave function: Psi(x,t) = Asin(2piBx)e^(-iCt) for 0<x<1/2B Psi(x,t) = 0 for all other...
Consider the following wave function: Psi(x,t) = Asin(2piBx)e^(-iCt) for 0<x<1/2B Psi(x,t) = 0 for all other x where A,B and C are some real, positive constants. a) Normalize Psi(x,t) b) Calculate the expectation values of the position operator and its square. Calculate the standard deviation of x. c) Calculate the expectation value of the momentum operator and its square. Calculate the standard deviation of p. d) Is what you found in b) and c) consistent with the uncertainty principle? Explain....
For the wave function ψ(x) defined by ψ(x)= A(a-x),x<a ψ(x)=0, x>=a (a) Sketch ψ(x) and calculate...
For the wave function ψ(x) defined by ψ(x)= A(a-x),x<a ψ(x)=0, x>=a (a) Sketch ψ(x) and calculate the normalization constant A. ( b) Using Zettili’s conventions, find its Fourier transform φ(k) and sketch it. (c) Using the ψ(x) and φ(k), make reasonable estimates for ∆x and ∆k. Using p = ħk, check whether your results are compatible with the uncertainty principle.
Consider the time-dependent ground state wave function Ψ(x,t ) for a quantum particle confined to an...
Consider the time-dependent ground state wave function Ψ(x,t ) for a quantum particle confined to an impenetrable box. (a) Show that the real and imaginary parts of Ψ(x,t) , separately, can be written as the sum of two travelling waves. (b) Show that the decompositions in part (a) are consistent with your understanding of the classical behavior of a particle in an impenetrable box.
The state of a particle is completely described by its wave function Ψ(?,?) One-dimensional Schrodinger Equation--...
The state of a particle is completely described by its wave function Ψ(?,?) One-dimensional Schrodinger Equation-- answer the following questions: 2) Show that when U(x) = 0, and , is a solution to the one-?=2??/ℏΨ=?sin??dimensional Schrodinger equation. 3) Show that when U(x) = 0, and , is a solution to the one-?=2??/ℏΨ=?cos??dimensional Schrodinger equation. 4) Show that where A and B are constants is a solution to the Ψ=??+?Schrodinger equation when U(x) = 0, and when E = 0.
A particular positron is restricted to one dimension and has a wave function given by ψ(x)=...
A particular positron is restricted to one dimension and has a wave function given by ψ(x)= Ax between x = 0 and x = 1.00 nm, and ψ(x) = 0 elsewhere. Assume the normalization constant A is a positive, real constant. (a) What is the value of A (in nm−3/2)? nm−3/2 (b) What is the probability that the particle will be found between x = 0.290 nm and x = 0.415 nm? P = (c) What is the expectation value...
Problem 7-3. Show that the wave function ψ given by Eq. (7-6) satisfies the boundary conditions...
Problem 7-3. Show that the wave function ψ given by Eq. (7-6) satisfies the boundary conditions given by Eq. (7-5) if the values of kx, ky, and kz are restricted to those of Eq. (7-7). Eq. ( 7- 5 ) : ψ( x + L , y, z,t) = ψ(x, y, z, t), ψ(x, y + L ,s,t) = ψ(x, y, z, t), ψ(x, y, z + L , t) = ψ(x, y, z, t). Eq. ( 7-6 ) :...