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majed_q8i
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Ever two-particle wave function is a product of two one-particle wave functions.
Is this true?
if not, can you give me a example ?
Thank you :)
Is this true?
if not, can you give me a example ?
Thank you :)
majed_q8i said:Ever two-particle wave function is a product of two one-particle wave functions.
Is this true?
if not, can you give me a example ?
Thank you :)
majed_q8i said:Ever two-particle wave function is a product of two one-particle wave functions. Is this true? if not, can you give me a example ?
alxm said:It's not true any time those two particles are interacting. If your wave function is a product of two single-particle functions, then every observable quantity is a product of the probabilities for the respective particles. I.e. they're statistically uncorrelated and so, independent of each other.
RedX said:Is the converse true? That is, if they're statistically uncorrelated, can they be written as a direct product?
alxm said:Statistical non-correlation means that P(A|B) = P(A)P(B), so yes.
I might want to add to the earlier that any set of interacting (correlated) particles may still be written as a linear expansion of different single-particle functions though. (Handwaving: Throw out the interaction terms from the Hamiltonian and solve for the single particles which can be used as a basis for the interacting Hamiltonian. E.g. a Slater determinant)
A two-particle wave function is a mathematical representation of the spatial and temporal behavior of a system composed of two particles. It describes the probability of finding the two particles at a given location and time, and includes information about the particles' properties such as spin and energy.
In quantum mechanics, particles are described by wave functions that evolve over time according to the Schrödinger equation. The two-particle wave function is a solution to this equation that describes the behavior of a system with two interacting particles.
Yes, the two-particle wave function can be used to calculate the probability of finding the two particles in a particular state at a given time. By solving the Schrödinger equation, the wave function can also provide information about the system's energy levels and how they change over time.
The shape of the two-particle wave function determines the probability of finding the particles in a particular region of space. A higher probability in one area means that the particles are more likely to be found there, while a lower probability means they are less likely to be found in that region.
The two-particle wave function does not take into account the effects of relativity and cannot accurately describe the behavior of particles moving at high speeds. It also does not account for interactions with external forces, such as electromagnetic fields. Additionally, the wave function only provides statistical predictions and cannot predict the exact behavior of individual particles.