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

[Yedi]

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)

 

[kuruman]

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 Schrödinger equation have to say about that?

 

[Dickfore]

Because those states are not normalizable.

 

[kuruman]

Because those states are not normalizable.

Sure.