Quantum Mechanics and Observables

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Discussion Overview

The discussion revolves around the nature of observables in quantum mechanics, specifically whether all observables are quantized and the implications of different potentials on energy levels. The scope includes theoretical concepts and interpretations within quantum mechanics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants propose that while observables in quantum mechanics are represented by operators, this does not necessarily imply that all observables are quantized.
  • Others argue that operators can have a continuous spectrum, suggesting that some observables may take on continuous values, as exemplified by the energy of a free particle.
  • A participant questions whether the energy of a particle becomes quantized when it is in a potential, leading to a discussion about the nature of different potentials.
  • It is noted that for certain potentials, such as those not bounded from above, energy can be quantized, while other potentials may lead to a mix of quantized bound states and continuous scattering states.

Areas of Agreement / Disagreement

Participants express differing views on the quantization of observables, with some asserting that not all observables are quantized and others providing examples that illustrate conditions under which quantization occurs. The discussion remains unresolved regarding the generality of quantization across all observables.

Contextual Notes

The discussion highlights limitations in understanding the conditions under which observables are quantized, particularly in relation to the types of potentials involved and the definitions of bound versus unbound states.

quantumfoam
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Hi guys! I have one question! I know that in quantum mechanics, observables must be in the form of operators. However, does that mean that all observables are quantized in quantum mechanics?
 
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quantumfoam said:
Hi guys! I have one question! I know that in quantum mechanics, observables must be in the form of operators. However, does that mean that all observables are quantized in quantum mechanics?

No. Operators can have continuous spectrum, so the observables may by continuous. This is the case of energy of a free particle for example.
 
Oh okay! So if the particle was in a potential then the energy of the particle would be quantized?
 
quantumfoam said:
Oh okay! So if the particle was in a potential then the energy of the particle would be quantized?

That's true for potentials that are not bounded from above (e.g. the harmonic oscillator potential). Some potentials, like that of an electron interacting with a proton, result in a set of quantized bound states with negative energy and a continuum of unbound "scattering states" with positive energy.
 
Last edited:
I see.(: Thanks guys!
 

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