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

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Homework Help Overview

The discussion revolves around the concept of energy states for free particles in quantum mechanics, specifically addressing the question of why negative energy states do not correspond to physical states or proper wave functions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of negative energy states, questioning the relationship between energy and potential energy for free particles. There is a discussion about the normalizability of these states and the role of the Schrödinger equation in this context.

Discussion Status

The conversation includes various perspectives on the nature of negative energy states, with some participants affirming that such states are not normalizable. There is an ongoing exploration of the implications of potential energy being zero for free particles.

Contextual Notes

Participants note the assumption that for a free particle, the potential energy is zero, which raises questions about the existence of states with energy less than this potential. The discussion reflects on the constraints imposed by the Schrödinger equation regarding these energy states.

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 Schrödinger 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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