Why Can't Free Particles Have Negative Energy States in Quantum Mechanics?

Yedi
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Why is there, for a free particle no physical state, i.e, proper wave function, for a negative energy?

Is it because k is imaginary? (k = sqrt(-2mE)/(reduced Planck's constant)
 
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Don't forget that, for a free particle, the potential energy is implicitly V = 0. Can a free particle exist in a state where its energy E is everywhere in space less than its potential energy? What does the Schrodinger equation have to say about that?
 
Because those states are not normalizable.
 
Dickfore said:
Because those states are not normalizable.
Sure.
 

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