The discussion revolves around the addition of wave functions in quantum mechanics, particularly in the context of describing systems with multiple particles. Participants explore the implications of combining individual wave functions and the mathematical frameworks involved, such as tensor products and probability rules.
Participants express differing views on how wave functions can be combined, with some advocating for addition and others emphasizing the necessity of tensor products. The discussion remains unresolved regarding the correct approach to combining wave functions for multiple particles.
The discussion highlights potential limitations in understanding the mathematical formalism of quantum mechanics, particularly concerning the definitions and operations applied to wave functions. There are unresolved aspects regarding the application of probability rules in this context.
Not added. One must form the "tensor product" of the two Hilbert spaces.ashutoshsharma said:the wave functions of individual particles can be added together to create a wave function for for system,
tom.stoer said:Consider a single particle wave function ψ(x) for a single particle. Adding two such wave functions ψa(x) + ψb(x) still describes one single particle.
In order to describe two particles you have to introduce two positions x and y and you have to use the product ψa(x) * ψb(y)