What are pure and mixed states in quantum mechanics?

In summary, a pure eigenstate refers to a state of a particle that is represented by a positive operator with a unit trace. These states are either pure, represented by the form |u><u|, or mixed, represented by the form ∑ pi |ui><ui|. It can be proven that all states fall into one of these two categories.
  • #1
aveline de grandpre
10
1
what does it mean that a particle is a pure eigenstate?
could someone explain this to me simply ?
 
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You'll have to give some context as to where you read that.
 
  • #3
aveline de grandpre said:
what does it mean that a particle is a pure eigenstate?
could someone explain this to me simply ?

I have tried and tried to simply explain it failing every time.

Here is the answer.

States are positive operators of unit trace. States of the form |u><u| are called pure. States of the form ∑ pi |ui><ui| are called mixed. It can be shown all states are pure or mixed. If that is gibberish then sorry its the best I can do - explaining linear algebra in English is impossible.

Thanks
Bill
 
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1. What is a pure eigenstate?

A pure eigenstate is a quantum state that has a definite value for a particular observable, such as position or momentum. It is an eigenvector of the corresponding operator, meaning that when the operator acts on the state, the resulting state is a scalar multiple of the original state.

2. How is a pure eigenstate different from a mixed state?

A pure eigenstate is a quantum state that is in a single, definite state, while a mixed state is a combination of two or more pure states with different probabilities. A pure eigenstate has a probability of 1 for a particular outcome when measured, while a mixed state has probabilities for multiple outcomes.

3. Are all quantum states pure eigenstates?

No, not all quantum states are pure eigenstates. A pure eigenstate is a special case where the state is in a single, definite state. Most quantum states are mixed states, which are combinations of pure eigenstates.

4. Can a pure eigenstate change over time?

In general, a pure eigenstate will not change over time. This is because the state is in a definite state and will remain in that state unless acted upon by an external force or measurement. However, in some cases, such as in the presence of a time-varying potential, a pure eigenstate can evolve into a different state.

5. How are pure eigenstates used in quantum mechanics?

Pure eigenstates are used in quantum mechanics to describe the state of a quantum system at a particular time. They are also used to calculate the probabilities of measuring different outcomes when the system is measured. Pure eigenstates are an important concept in understanding the behavior of quantum systems and are essential in many quantum algorithms and applications.

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