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Nickyv2423

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In summary: More precisely there cannot be interference because probabiity is assumed to follow normalised matter density ##\rho##. The mapping from phase space to probability is not the same as in QT.

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Nickyv2423

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houlahound

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DrClaude

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That's not correct. The wave function must always be normalizable, which is why a plane wave is not a valid state for an electron, and a superposition of plane waves (wave packet) is needed to correctly describe the state of a free particle.hilbert2 said:but the free electron wavefunction doesn't have to be normalizable like the wavefunction of a confined electron.

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houlahound

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Anyhoo good luck finding a region in the universe that is field free to support a free electron. Free particles seem mythical in the strict sense in my amateur opinion.

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Nugatory

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houlahound said:Anyhoo good luck finding a region in the universe that is field free to support a free electron. Free particles seem mythical in the strict sense in my amateur opinion.

It's easy to find free electrons: CRT displays, pre-flatscreen TV sets, vacuum tubes, lightning, static discharges... Electrons are so mobile that free electrons are responsible for almost all the transfers of electric charge that we see in daily life.

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Nugatory

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Not correct. A particle is free if its total energy (kinetic plus potential) is positive when using the convention that the potential at infinity is zero.houlahound said:Not to be pedantic but is it correct to say a wave packet is not a free particle because it has to be in a potential to be in a superposition state.

Whether it's free or bound has nothing to do with superposition, and there is no such thing as a quantum state that is not a superposition in some basis.

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houlahound

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I have never seen a formal definition of free, I figured it must be free of all fields which excludes even weak fields relative the particles energy.

I guess you are saying an electron is free if it is ionised. Not trying to make up my own definitions but free is a pretty in accurate term the way you have defined it.

All electrons are in a gravity energy well at least, hence minimally bound.

Oh well my definition is wrong, I learned something.

If I was more adept I would like to calculate how gravity effects the spectra of a particle in a box problem, know any links for that?

BTW will start a separate thread re superposition.

I guess you are saying an electron is free if it is ionised. Not trying to make up my own definitions but free is a pretty in accurate term the way you have defined it.

All electrons are in a gravity energy well at least, hence minimally bound.

Oh well my definition is wrong, I learned something.

If I was more adept I would like to calculate how gravity effects the spectra of a particle in a box problem, know any links for that?

BTW will start a separate thread re superposition.

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DrClaude said:That's not correct. The wave function must always be normalizable, which is why a plane wave is not a valid state for an electron, and a superposition of plane waves (wave packet) is needed to correctly describe the state of a free particle.

To put it more exactly, in the case of a confined electron, unnormalizable position repr. wavefunctions don't appear even as a mathematical tool in the eigenfunction expansions of the wavepackets.

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https://arxiv.org/abs/quant-ph/0505143

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Demystifier said:

https://arxiv.org/abs/quant-ph/0505143

That's quite cool... So the positivity of this classical wavefunction (mentioned in the abstract) prevents interference phenomena from happening in the classical case?

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Exactly!hilbert2 said:That's quite cool... So the positivity of this classical wavefunction (mentioned in the abstract) prevents interference phenomena from happening in the classical case?

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Mentz114

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More precisely there cannot be interference because probabiity is assumed to follow normalised matter density ##\rho##. The mapping from phase space to probability is not the same as in QT.hilbert2 said:That's quite cool... So the positivity of this classical wavefunction (mentioned in the abstract) prevents interference phenomena from happening in the classical case?

A wave function is a mathematical description of the quantum state of a system. It represents the probability amplitude of finding a particle in a particular location or state.

In quantum mechanics, quantization refers to the restriction of certain physical quantities, such as energy or angular momentum, to discrete values. The wave function describes the quantized state of a system, where the particle's position and momentum can only take on certain values.

Yes, in quantum mechanics, all particles have both a wave-like and a particle-like nature. This means that they can exhibit wave-like properties, such as being quantized, while also behaving like a localized particle with a specific position and momentum.

No, the wave function is a fundamental aspect of quantum mechanics and is used to describe the behavior of all particles. If an object is not quantized, it means that its energy or other physical quantities can take on any value, which goes against the principles of quantum mechanics.

The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time. The wave function incorporates this principle by representing the probability of finding a particle in a particular location or state, rather than its exact position or momentum.

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