Referring to the attached set of equations,
Wave function of the "Schrodinger equation for two-particles [equation 1]" can be separated using separation of variable method, when they are distinguishable. And two separate "one particle" equations must be [equation 3]. In this form, the physical meaning must be, the particle 1 is in the potential field "V", and particle 2 feels no potential at all, unless I assume V=V1+V2 where particle 1 is in facing V1 and particle 2 is facing V2 potential. I mean V1 and V2 could be any real value that I choose!!!! But is it?
However for distinguishable particles this mathematical derivation is fairly simple. But how people come up with the composite wave function for indistinguishable particles [equation 4]? Is it just a guess or there is any formal mathematical derivation?
This is a good question.
A helpful introduction to the particle wave function, its formulation, derivation and application, is given in the papers by Rickard Armiento here on RG:
https://www.researchgate.net/profile/Rickard_Armiento
Armiento's Ph.D. thesis
The many-electron energy in density functional theory, thesis, KTH school of engineering sciences, Stockholm, Sweden, 2005
downloadable from the web.
More to the point, see Armiento's book available on RG at
https://www.researchgate.net/publication/233832374_The_Many-Electron_Energy_in_Density_Functional_Theory_From_Exchange-Correlation_Functional_Design_to_Applied_Electronic_Structure_Calculations
Book The Many-Electron Energy in Density Functional Theory, From ...
- Badges
- Science topic
- Similar topics
- Mathematics