Is a Pseudo-Wavefunction Really a Mixed State?

In summary, the conversation discussed the concept of pseudopotentials and the relationship between the pseudo-wavefunction and the original Hamiltonian. It was mentioned that pseudopotentials remove nodes near the core, resulting in a pseudo-wavefunction that resembles a lower energy state. The possibility of representing the pseudo-wavefunction as a sum of core and valence states was also brought up. However, there was also doubt about the completeness of the all-electron basis in representing the pseudo-wavefunction.
  • #1
Modey3
135
1
Hello,

I'm studying pseudopotentials right now, and I had an epiphany that the pseudo-wavefunction is really mixed-state of the original Hamiltonian. Has anyone ever thought about a pseudo-wavefunction that way? Just curious.

modey3
 
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  • #2
I'm don't think that's correct. Pseudopotentials remove nodes that are near the core, so a pseudopotential for Nb (say) will have 4d valence states, however the 4d states will not have a node near the core so they really will look like 3d states. I don't think you can accomplish elimination of a node by mixing states with n > 4.
 
  • #3
kanato,

If you take the overlap integral between the pseduo-wavefunction and a particular all-electron valence and the core wavefunctions you get non-zero terms. This means that the pseudo wavefunction can be represented as a sum of core-states and the valence states each scaled by their overlaps with the pseduo-wavefunction. The OPW-method does this.
 
  • #4
Sure, there's non-zero overlap, but I am unconvinced as to whether the all-electron basis is "complete enough" to represent the pseudo-wavefunction.
 

Related to Is a Pseudo-Wavefunction Really a Mixed State?

1. What is a pseudo-wavefunction?

A pseudo-wavefunction is a mathematical construct used in quantum mechanics to describe a system that is in a mixed state. It is a combination of two or more distinct quantum states, each with a certain probability of being observed.

2. How is a pseudo-wavefunction different from a regular wavefunction?

A regular wavefunction describes a system that is in a pure state, meaning that it is in one well-defined quantum state with a probability of 1. A pseudo-wavefunction, on the other hand, describes a system that is in a mixed state, meaning that it is a combination of two or more distinct quantum states with different probabilities.

3. Can a pseudo-wavefunction be observed or measured?

No, a pseudo-wavefunction is a mathematical concept and cannot be directly observed or measured. However, the probabilities associated with each quantum state in the pseudo-wavefunction can be measured through physical experiments.

4. How is a pseudo-wavefunction used in quantum mechanics?

In quantum mechanics, a pseudo-wavefunction is used to describe systems that are in a mixed state, such as entangled particles or systems with unknown or uncertain properties. It allows for the calculation of probabilities for different outcomes of measurements on the system.

5. Is a pseudo-wavefunction a valid representation of a physical system?

Yes, a pseudo-wavefunction is a valid mathematical representation of a physical system in quantum mechanics. It is a useful tool for understanding and predicting the behavior of systems that are in a mixed state.

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