The addition of the wave functions for a system

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The discussion centers on how to construct a wave function for a system of multiple particles in quantum mechanics. It clarifies that individual wave functions cannot simply be added; instead, the tensor product of their respective Hilbert spaces must be used. For two particles, their wave functions are represented as a product of functions, ψa(x) * ψb(y), rather than a sum. This method allows for the proper description of systems with multiple particles, despite their differing wave functions. The conversation also touches on the role of probability in quantum mechanics, suggesting it underlies these operations.
ashutoshsharma
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the wave functions of individual particles can be added together to create a wave function for for system, that means quantum theory allows physicists to examine many particles at once??...how is it possible if the wave function of each particles is different??...is it based on rules of probability??
 
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ashutoshsharma said:
the wave functions of individual particles can be added together to create a wave function for for system,
Not added. One must form the "tensor product" of the two Hilbert spaces.
 
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)
 
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)

and isn't it guided by the rules of probability?
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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