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.
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.
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.
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.
Demystifier said:It is possible to introduce a classical wave function in classical statistical physics:
https://arxiv.org/abs/quant-ph/0505143
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?
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.