- #1

- 51

- 0

Note this is more of a coursework understanding question rather than a specific homework question.

I have been reading about matter waves and de Broglie relations which suggest that electrons can act as waves. From wikipedia (http://en.wikipedia.org/wiki/Matter_wave) it suggests that the following is true.

[tex]\lambda = \frac{h}{p}[/tex] and [tex]f = \frac{E}{h}[/tex]

In that article it does not suggest the significance of the amplitude in the matter wave. From the wave–particle duality article (http://en.wikipedia.org/wiki/Wave–particle_duality) it suggests that "upon measuring the location of the particle, the wave-function will randomly "collapse" to a sharply peaked function at some location, with the likelihood of any particular location equal to the squared amplitude of the wave-function there."

If I understand this correctly, the probability of finding an ejected electron along a linear trajectory is not equal along its path, but rather the probability is sinusoidal. At one part of the trajectory, I might have a 100% chance of finding an electron when the amplitude is max and [tex]\lambda [/tex]/4 away there is a 0% chance of finding an electron when the amplitude is zero. This is counterintuitive so I want to check if my reasoning is correct.

Thanks in advance.

PS: For a numerical example, solving the equations for an electron in a 10 kV scanning electron microscope yields a wavelength of 12.3 x 10^-12 m (12.3 pm) as from http://en.wikipedia.org/wiki/Electron_diffraction. If I understand this correctly, as an electron travels in this setup, the probability of finding the electron varies from 0% to 100% sinusoidally with a wavelength of 12.3 x 10^-12 m (12.3 pm).

## Homework Statement

I have been reading about matter waves and de Broglie relations which suggest that electrons can act as waves. From wikipedia (http://en.wikipedia.org/wiki/Matter_wave) it suggests that the following is true.

[tex]\lambda = \frac{h}{p}[/tex] and [tex]f = \frac{E}{h}[/tex]

In that article it does not suggest the significance of the amplitude in the matter wave. From the wave–particle duality article (http://en.wikipedia.org/wiki/Wave–particle_duality) it suggests that "upon measuring the location of the particle, the wave-function will randomly "collapse" to a sharply peaked function at some location, with the likelihood of any particular location equal to the squared amplitude of the wave-function there."

## The Attempt at a Solution

If I understand this correctly, the probability of finding an ejected electron along a linear trajectory is not equal along its path, but rather the probability is sinusoidal. At one part of the trajectory, I might have a 100% chance of finding an electron when the amplitude is max and [tex]\lambda [/tex]/4 away there is a 0% chance of finding an electron when the amplitude is zero. This is counterintuitive so I want to check if my reasoning is correct.

Thanks in advance.

PS: For a numerical example, solving the equations for an electron in a 10 kV scanning electron microscope yields a wavelength of 12.3 x 10^-12 m (12.3 pm) as from http://en.wikipedia.org/wiki/Electron_diffraction. If I understand this correctly, as an electron travels in this setup, the probability of finding the electron varies from 0% to 100% sinusoidally with a wavelength of 12.3 x 10^-12 m (12.3 pm).

Last edited: