Question

Consider a particle in a 1‐D quantum mechanical model. Show that the second derivatives of the...

Consider a particle in a 1‐D quantum mechanical model. Show that the second derivatives of the wave functions of the particle are continuous if V(x) is a continuous function. Will you obtain a different conclusion if V(x) is NOT a continuous function? Here, you can assume that V(x) is a finite function.

Homework Answers

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
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.
Intro to Quantum Mechanics (Free particle) a). Write the relations between the wave vector and angular...
Intro to Quantum Mechanics (Free particle) a). Write the relations between the wave vector and angular frequency of a free particle and its momentum vector and energy. b) What is the general form in one dimension of the wave function for a free particle of mass m and momentum p? c) Can this wave function ever be entirely real? If so, show how this is possible. If not, explain why not. d) What can you say about the integral of...
1) *Particles & waves in free space* a) Consider a particle with mass m travelling through...
1) *Particles & waves in free space* a) Consider a particle with mass m travelling through free space with velocity v. What is momentum of the particle? What is the kinetic energy of the particle? b) In quantum mechanics, any particle can be represented as a wave. What are the wavelength and frequency associated with the particle in part a? c) Now consider a beam of light propagating in a vacuum. The wavelength of the light is 500nm. What is...
The sides of a one dimensional quantum box (1-D) are in x=0, x=L. The probability of...
The sides of a one dimensional quantum box (1-D) are in x=0, x=L. The probability of observing a particle of mass m in the ground state, in the first excited state and in the 2nd excited state are 0.6, 0.3, and 0.1 respectively a) If each term contributing to the particle function has a phase factor equal 1 in t=0. What is the wave function for t>0? b) what is the probability of finding the particle at the position x=L/3...
Consider the function f : R → R defined by f(x) = ( 5 + sin...
Consider the function f : R → R defined by f(x) = ( 5 + sin x if x < 0, x + cos x + 4 if x ≥ 0. Show that the function f is differentiable for all x ∈ R. Compute the derivative f' . Show that f ' is continuous at x = 0. Show that f ' is not differentiable at x = 0. (In this question you may assume that all polynomial and trigonometric...
We have examined the Particle in a Box problem in one dimension, meaning that we consider...
We have examined the Particle in a Box problem in one dimension, meaning that we consider only one variable, x. We can go to higher dimensions, for example, we can consider what this would look like if we wanted to think about both x and y. In that case we would need to make some changes. The potential energy V(x) would become V(x,y), but would behave in a similar way as before. It would equal infinity if either x or...
Consider a function F=u+iv which is analytic on the set D={z|Rez>1} and that u_x+v_y=0 on D....
Consider a function F=u+iv which is analytic on the set D={z|Rez>1} and that u_x+v_y=0 on D. Show that there exists a real constant p and a complex constant q such that F(z)=-ipz+q on D. Notation: Here u_x denotes the partial derivative of u with respect to x and v_y denotes the partial derivative of v with respect to y.
Consider a Li++ ion as described by the Bohr model. (a) At some other time, the...
Consider a Li++ ion as described by the Bohr model. (a) At some other time, the electron in n=4 state. What possible wavelength of radiation emitted by this atom? Write the algebraic expression(s) and draw the diagram to illustrate the transitions. (b) What is the ground state energy of this system in eV? Write the expression and evaluate it. What value of the quantum number n does this correspond to? (c) Now assume the electron is in the n=1 state....
1. Consider the function f(x) = 2x^2 - 7x + 9 a) Find the second-degree Taylor...
1. Consider the function f(x) = 2x^2 - 7x + 9 a) Find the second-degree Taylor series for f(x) centered at x = 0. Show all work. b) Find the second-degree Taylor series for f(x) centered at x = 1. Write it as a power series centered around x = 1, and then distribute all terms. What do you notice?
II(20pts). Short Problems a) The lowest energy of a particle in an infinite one-dimensional potential well...
II(20pts). Short Problems a) The lowest energy of a particle in an infinite one-dimensional potential well is 4.0 eV. If the width of the well is doubled, what is its lowest energy? b) Find the distance of closest approach of a 16.0-Mev alpha particle incident on a gold foil. c) The transition from the first excited state to the ground state in potassium results in the emission of a photon with  = 310 nm. If the potassium vapor is...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT