Wikipedia's derivation of the Schrodinger equation apparently includes the premise that the energy of a particle is the product of Planck's constant and the particle's frequency.(adsbygoogle = window.adsbygoogle || []).push({});

E = hf

I have seen this equation before for photons but when applied to matter, I'm confused. If we assume the following

[tex] E = \frac {p^2}{2m} [/tex]

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

[tex] p = mv [/tex]

[tex] \lambda f = v [/tex]

where

E = energy

p = momentum

m = mass

λ = wavelength

f = frequency

v = velocity

simple algebraic manipulation yields E = hf/2 , not hf. The only relationship not mentioned in the derivation is the λf = v, but how could that not be true for a wave of any kind?

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# Kinetic energy of matter

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