Consider a stationary solution of the Schrodinger Equation with positive energy E for a particle with...

Consider a stationary solution of the Schrodinger Equation with positive energy E for a particle with mass m in the following one-dimensional potential: V (x) = 0 for |x| > a and V (x) = −V0 for |x| ≤ a with V0 > 0. (a) Calculate the transmission and reflection probabilities. (b) Show that the transmission probability is unity for some values of the energy.

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Solve the time independent schrodinger equation for a particle confined to a mobius strip.

1. Write the Schrodinger equation for particle on a ring, and rearrange it until you have...

1. Write the Schrodinger equation for particle on a ring, and rearrange it until you have the following: ? 2? ??2 = − 2?? ℏ 2 ? … a) Assuming that ?? 2 = 2?? ℏ 2 , (where ml is a quantum number and has nothing to do with mass), show that the following is a solution for the Schrodinger equation you obtained: ?(?) = ? ? ????… b)Now think about bounds of variable ?. Using that argue that...

1. A particle satisfying the time-independent Schrodinger equation must have a) an eigenfunction that is normalized....

1. A particle satisfying the time-independent Schrodinger equation must have a) an eigenfunction that is normalized. b) a potential energy that is independent of location. c) a de Broglie wavelength that is independent of location d) a total energy that is independent of location. Correct answer is C but I need detailed explanation also explain each point why they are false

Use the Schrodinger equation solution of the H atom corresponding to its wave function for the...

Use the Schrodinger equation solution of the H atom corresponding to its wave function for the 3dxy orbital to explain why this orbital has no radial node. Questions to consider: (j) What is the value of the wave function and thus the radial part of the function at a node? (ii) What factor of the radial part of the wave function, containing r, can equal your value in (i) and thus allow you to obtain a value for r?

IP An α particle with a kinetic energy of 0.45 MeV approaches a stationary gold nucleus....

IP An α particle with a kinetic energy of 0.45 MeV approaches a stationary gold nucleus. A)What is the speed of the α particle? (To obtain the mass of an alpha particle, subtract the mass of two electrons from the mass of 4/2He. ) Express your answer using two significant figures. v= ___ m/s B)What is the distance of closest approach between the αα particle and the gold nucleus? d= ___pm C)If this same αα particle were fired at a...

Determine the Time-Dependent Schrodinger Equation (TDSE) from the classical non-relativistic expression for the energy of a...

Determine the Time-Dependent Schrodinger Equation (TDSE) from the classical non-relativistic expression for the energy of a particle and de Broglie’s claim that all particles can be represented as waves. (Important: Describe as much as possible and must use your own words to explain it.)

(a)What equation gives the wavelength of a particle? (b) What equation gives the energy of the...

(a)What equation gives the wavelength of a particle? (b) What equation gives the energy of the n=4 level of the hydrogen atom? In your equation write RH as RH. (c) What is the equation for the frequency of light when the Hydrogen atom makes a transition from n=4 to n=2? Evaluate everything but RH and h. Thank you so much!

1a. A positive particle of charge 5 C sits stationary [locked to the ground] 3.5 meters...

1a. A positive particle of charge 5 C sits stationary [locked to the ground] 3.5 meters from a negatively charged particle, with charge 2 C. How strong is the force the negative particle experiences? How does that compare if the negative particle is 7 meters away? Both charges have mass of 5 grams; how fast does the negatively charged particle accelerate in both cases? b. What force does a particle with a charge of +5 C, moving at 10 m/s...

Consider the nonhomogeneous equation y"-8y'+16y=e^4x cos x. Find a particular solution of the equation by the...

Consider the nonhomogeneous equation y"-8y'+16y=e^4x cos x. Find a particular solution of the equation by the method undetermined coefficients.

Suppose a solution to the time independent Schrodinger equation is multiplied by exp(-iEt/h-bar), thus making it...

Suppose a solution to the time independent Schrodinger equation is multiplied by exp(-iEt/h-bar), thus making it a solution to the time dependent Schrodinger equation. Will the product still be a solution to the time independent equation?

Subjects