Direction of momentum given by the de Broglie relation p = m v where m is th

Waylon Mcbride

Waylon Mcbride

Answered question

2022-05-07

Direction of momentum given by the de Broglie relation
p = m v
where m is the mass of an electron, and v is its velocity. In this case, since v is a vector, it's clear that the momentum will be also a vector.
However if the momentum is a vector quantity (and it is), what is the direction of the electron's momentum given by the de Broglie relation
p = h / λ p = k
if the Planck constant h is scalar and the wavelength λ is also scalar. Similarly the reduced Planck constant is scalar and the wavenumber k = 2 π / λ is also scalar.

Answer & Explanation

tomatoland45wt8wm

tomatoland45wt8wm

Beginner2022-05-08Added 19 answers

In general the wavenumber is a vector. That is, e i ( k x ω t ) is a solution to the wave equation in 3 (or any number) dimensions. We say this solution is a plane wave propagating in the k ^ direction with wavenumber | k | or wavelength λ = 2 π / | k |
So properly the de Broglie relation is p = k . The momentum of a plane wave is in the same direction as the propagation of the wave.

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