(a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm-¹)? Express your answer in scientific notation with three significant figures. (b) The Hamiltonian operator for a free electron is given by ħ² d² Ĥ = ô² 2me 2m dx² The wave function provided at the top is an eigenstate of Â. If one measures the energy for an electron in this state using π, what would be the result, and how does it compare to the classical kinetic energy of a free electron with this velocity? =
(a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm-¹)? Express your answer in scientific notation with three significant figures. (b) The Hamiltonian operator for a free electron is given by ħ² d² Ĥ = ô² 2me 2m dx² The wave function provided at the top is an eigenstate of Â. If one measures the energy for an electron in this state using π, what would be the result, and how does it compare to the classical kinetic energy of a free electron with this velocity? =
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:A free electron moving along the x-direction (one for which V(x) = 0) would have a wave
function of the form
f(x) = A eikx + B e−ikx
where A and B are constants.
(a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of
the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm¯¹)?
Express your answer in scientific notation with three significant figures.
(b) The Hamiltonian operator for a free electron is given by
p²
ħ² d²
Ĥ
2me
2me dx²
The wave function provided at the top is an eigenstate of Â. If one measures the energy
for an electron in this state using Â, what would be the result, and how does it compare
to the classical kinetic energy of a free electron with this velocity?
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