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Question
The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
E = hv, p = `"h"/lambda`
But while the value of λ is physically significant, the value of v (and therefore, the value of the phase speed vλ) has no physical significance. Why?
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Solution
The absolute value of the energy of a particle is arbitrary within the additive constant. Hence, wavelength (λ) is significant, but the frequency (v) associated with an electron has no direct physical significance.
Therefore, the product νλ(phase speed)has no physical significance.
Group speed is given as:
`"v"_"G" = ("dv")/("dk")`
= `"dv"/("d"(1/lambda)) = "dE"/"dp" = ("d"("p"^2/2"m"))/"dp" = "p"/"m"`
This quantity has a physical meaning.
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