Special conditions of a wavefunction?

In summary, the question asks about the conditions under which a wavefunction that depends on a series of coordinates can be written as a product of wavefunctions that only depend on one coordinate each. It is likely that the Hamiltonian plays a role in this case, as the question also mentions energy. If the Hamiltonian is the sum of single-particle operators that commute with each other, then a product wavefunction can satisfy the Schrodinger equation and have a total energy equal to the sum of the single-particle energies.
  • #1
MontavonM
7
0
Under what special conditions can a wavefunction that depends on a series of coordinates be written as a product of wavefunctions that only depend on one coordinate each? What can you say about the energy in this case? (This is a study/end of the chapter question (P.Chem))... I'm thinking it's when the product wavefunction's operators commute with each other, which would make the energy zero... I'm just wanting to check. Thanks in advance
 
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  • #2
MontavonM said:
... I'm just wanting to check. Thanks in advance

no, that is not correct
 
  • #3
any pointers/help you could give me?
 
  • #4
I think the question is worded very poorly, but probably they are looking for some statement about the Hamiltonian since they also ask about energy. For example, if the hamiltonian is the sum of single-particle operators (operators only depending on a single coordinate and momentum) then a product wavefunction can still satisfy the schrodinger equation and the total energy is the sum of the single particle energies...
 
  • #5
Thank you for the help!
 

Related to Special conditions of a wavefunction?

1. What is a wavefunction?

A wavefunction is a mathematical function that describes the quantum state of a particle or system. It contains information about the position, momentum, and other physical properties of the particle.

2. What are special conditions of a wavefunction?

Special conditions of a wavefunction refer to certain constraints or requirements that must be met in order for the wavefunction to accurately describe the quantum state of a particle or system. These conditions may include normalization, continuity, and single-valuedness.

3. Why are special conditions of a wavefunction important?

Special conditions of a wavefunction are important because they ensure that the wavefunction is physically meaningful and can accurately describe the quantum state of a particle or system. Without these conditions, the wavefunction may not accurately represent the behavior of the particle.

4. How do special conditions of a wavefunction affect the behavior of a particle?

The special conditions of a wavefunction determine the possible values of physical properties (such as position and momentum) that the particle can have. They also determine the probability of the particle having a certain value for a given property.

5. Are there different sets of special conditions for different types of wavefunctions?

Yes, there are different sets of special conditions for different types of wavefunctions. For example, the special conditions for a wavefunction describing a free particle may be different from those for a wavefunction describing a particle in a potential well. The specific conditions depend on the physical situation being described.

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