Is the Ground State of a System Always Pure?

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Physicist
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Hello

I read the following statement somewhere:

"... we study the entaglement of the ground state and the mixed state at finite temperatures ..."

Does this mean that the ground state of a system is always pure? :confused:

Thanks
 
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Any state that can be represented by a vector in the Hilbert space (e.g., any solution of the stationary Schroedinger equation, including the ground state solution) is a pure quantum state.

Eugene.
 
  • #3
Mixed state are important when you study statistical properties of a system. I.e. the density matrix describes the property of an ensemble (which is why the . Hence, a mixed state does not describe a "proper" state as such.
You can also get what is sometimes known as an "improper" mixture if you study a specific subsystem of a composite system by tracing out all other degrees of freedom.
 
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Double post
 
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FAQ: Is the Ground State of a System Always Pure?

What is a pure state in quantum mechanics?

A pure state in quantum mechanics refers to a state of a quantum system that can be described by a single wave function. This means that the exact energy and position of the system can be known with certainty.

How is a pure state different from a mixed state?

A mixed state, also known as a statistical mixture, is a combination of two or more pure states. In contrast to a pure state, a mixed state is characterized by a probability distribution of possible states and does not have well-defined energy or position.

Can a pure state change into a mixed state?

No, a pure state cannot change into a mixed state. According to the principles of quantum mechanics, a pure state will always remain a pure state and a mixed state will always remain a mixed state.

How are pure and mixed states represented mathematically?

In quantum mechanics, pure states are represented by a state vector, also known as a ket, which is an element of a complex vector space. Mixed states are represented by density matrices, which are mathematical objects that describe the probabilities of different pure states in a mixed state.

What are some real-life examples of pure and mixed states?

A pure state can be exemplified by a single photon, which has a well-defined energy and position. A mixed state can be seen in the state of a radioactive atom, which can decay into two different states with a certain probability, making it a mixture of two pure states.

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