I need help about a problem which seems trivial, but I would like to see material with experimental evidence.
It is clear that for a single-particle wave-function of, say, an electron, e.g.
(1) |ψ> = (1/√2) ( |a> + |b>),
the two wave-packets do not repel one another. For repelling one another, the wave-function should contain a term |a>|b>. A phylosopher of QM, named Shan Gao, inferred from this fact that the electron charge is not present at the same time in both |a> and |b>.
Gao's conclusion is of top importance in the efforts of understanding the meaning of the wave-function. But I would want to see some material on experiments proving that two parts of a single-particle wave-function do not interact
Can somebody recommend me some reference(s) to experiment(s) ?
Wave function, in quantum mechanics, variable quantity that mathematically describes the wave characteristics of a particle. The value of the wave function of a particle at a given point of space and time is related to the likelihood of the particle’s being there at the time. By analogy with waves such as those of sound, a wave function, designated by the Greek letter psi, Ψ, may be thought of as an expression for the amplitude of the particle wave (or de Broglie wave), although for such waves amplitude has no physical significance. The square of the wave function, Ψ2, however, does have physical significance: the probability of finding the particle described by a specific wave function Ψ at a given point and time is proportional to the value of Ψ2.
"Using the Wave Function. at the viewing screen (a distance D away), an interference pattern is produced (part (a) of the figure). Bright fringes correspond to points of constructive interference of the light waves, and dark fringes correspond to points of destructive interference of the light waves (part (b))." For a more elaborate meaning of the foregone, have a look at :
https://opentextbc.ca/universityphysicsv3openstax/chapter/wave-functions/
Dear Ijaz,
Thanks for your comment, but it does not address my question. For answering me I would appreciate reference to an experiment that shows that two parts of the wave-function of, say, an electron, do not repel one another. Or, something similar.
Dr Sofia --- The Double slit Expt:
Kindly have a look at the following useful links:
https://www.researchgate.net/post/Is-there-a-connection-between-the-electron-cycle-and-the-wave-particle-duality
https://www.researchgate.net/post/Why-is-wave-particle-duality-important
https://www.southampton.ac.uk/~doug/quantum_physics/quantum_physics.pdf
Are there "parts" that could interact? The question seems to misunderstand the nature of the probability function.
Julian Cockbain
Yes, there are parts. For instance, take an orbital of the electron around the nucleus of the atom. Does half of the orbital repel the other half?
Alternatively, consider an electron wave-function with two wave-packets. Would the wave-packets repel one another?
DR Sophia:
Hund's rule states that:
When assigning electrons to orbitals, an electron first seeks to fill all the orbitals with similar energy (also referred to as degenerate orbitals) before pairing with another electron in a half-filled orbital. Atoms at ground states tend to have as many unpaired electrons as possible. In visualizing this process, consider how electrons exhibit the same behavior as the same poles on a magnet would if they came into contact; as the negatively charged electrons fill orbitals, they first try to get as far as possible from each other before having to pair up.So there would be a repulsion in your case.
Regards--
Parts of 1 single orbital:
First of all my notion of orbitals was that they are nothing more than the path traversed by an electron and more that it is the wave of the electron spread around the nucleus .So going by that notion why is it that no two electrons with same spin can be present in an orbital ? is it because of the electromagnetic fields created by the electrons in same directions such that the fields will repel each other and electrons would not stay together.And if that is true why is it that the fields would repel each other when in the same direction and not when in opposite directions ?Further why not more than two fields could be present ,is it because no matter the direction any two fields would repel each other after all?
A short answer would be --the two halves of a single orbital would repel each other because of the fields embedded!!
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