Question

What does the relation between mass and energy of a free particle mean?

Answer 1

What does the Hamiltonian for a free particle mean? Does it mean that the kinetic energy of the particle is in reverse relation with mass? HH or E=ℏ2k2/2mE=ℏ2k2/2m.

Or better to ask: what's the relation between kk and mm

Answer 2

According to that theory, the energy of a moving particle (neglecting  any potential fields that may be present..So, no potential  energy..)  was not simply the kinetic energy known earlier, but something else..Something MORE.

Earlier the energy of a moving particle was the following:

E=p22mE=p22m  i.e the usual  12mv212mv2

'pp' is the momentum and equal to mvmv , where 'vv' is the velocity of the particle.

Here, the mass 'mm' was never thought to be affected by motion.

So, the mass of a moving particle, was taken same as the mass of the particle when the particle was at rest with respect to the observer. The rest mass.

So, earlier, it was thought that the mass of a moving particle was the same as that of the stationary particle.

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