moving along the x- function of the form (one for which v(x) 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 x 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 A = did have a wave
moving along the x- function of the form (one for which v(x) 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 x 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 A = did have a wave
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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 + Be -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 x 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
p²
2me
2m₂ 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?
Ĥ =
=
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