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What is $E$ in below equation? Does it represent total energy or kinetic energy(De-broglie equation for uncharged particle like neutron.)

Physics Asked on May 18, 2021

De-broglie equation for uncharged particle:
$$lambda= frac{h}{sqrt{2mE}}$$
Where,
$lambda$ = wavelength

$h$ = planks constant

$m$ = mass of uncharged particles

2 Answers

The de Broglie wavelength is the wavelength, $λ$, associated with a massive particle (i.e., a particle with mass, as opposed to a massless particle) and is related to its momentum, $p$, through the Planck constant, $h$:

$$lambda= frac{h}{p}$$

For non-relativistic particle, Total energy of free particle $$E=frac{p^2}{2m}Rightarrow p=sqrt{2mE}$$ $$lambda= frac{h}{sqrt{2mE}}$$


In relativistic-case, Using two formulas from special relativity, one for the relativistic mass-energy and one for the relativistic momentum

$$p=gamma m_0 v$$ $$Rightarrow lambda=frac{h}{gamma m_0 v}$$

Answered by Young Kindaichi on May 18, 2021

$E$ here is the kinetic energy, not the total energy.

The original formula is $lambda=h/p$, and then $p$ is obtained from the (non-relativistic) formula $E={1over 2} m v^2 = p^2/2m$

Answered by RogerJBarlow on May 18, 2021

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