Quantum Mechanics

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Questions and Answers

In quantum mechanics, what does the density matrix describe?

Pure states and their measurements
Expectation values of observables
Statistical and quantum averages for compound systems and entangled states (correct)
State vector in the Hilbert space

What characterizes a pure state in quantum mechanics?

Largest set of mutually commuting independent observables (correct)
Mean value of a quantum state
Expectation value of an operator
State vector as a pure state

How is a state vector defined in quantum mechanics?

Expectation value of an operator in a specific state
Average over an ensemble of members
Pure state that describes the system with maximum possible information (correct)
Quantum averages for compound systems

What does the mean/expectation value of an operator in a specific state represent in quantum mechanics?

Average over an ensemble of members all characterized by that same state vector (D) Signup and view all the answers

What is the purpose of the largest set of mutually commuting independent observables in quantum mechanics?

To completely and uniquely characterize a pure state (D) Signup and view all the answers

Explain the purpose of the density matrix in quantum mechanics.

The density matrix is a formalism that describes both statistical and quantum averages. It generalizes the concept of the state vector, allowing the description of compound systems or sub-systems that are parts of an entangled state. Signup and view all the answers

What is a pure state in quantum mechanics and how is it characterized?

A pure state in quantum mechanics is the most complete information of the quantum state. It is characterized by the largest set of mutually commuting independent observables, which when measured, characterize the state completely and uniquely. Signup and view all the answers

How is a state vector defined in quantum mechanics, and what does it describe?

A state vector is a pure state that describes the system with the maximum possible information. It cannot be further specified by additional measurements. The mean/expectation value of an operator in a specific state is interpreted as the average over an ensemble of members all characterized by that same state vector. Signup and view all the answers

What does the largest set of mutually commuting independent observables represent in quantum mechanics?

The largest set of mutually commuting independent observables represents the most complete information of the quantum state. Their measurements characterize the state completely and uniquely. Signup and view all the answers

How does the density matrix generalize the concept of the state vector in quantum mechanics?

The density matrix in quantum mechanics generalizes the concept of the state vector by allowing the description of compound systems or sub-systems that are parts of an entangled state, providing a formalism for both statistical and quantum averages. Signup and view all the answers

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