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ehrenfest
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Homework Statement
I am confused about Quick Calculation 11.3. What does he mean "by viewing x_0^I as the explicitly time-dependent Heisenberg operator defined by (11.38)"?
Specifically, what does "viewing" mean?
A time-dependent Heisenberg operator is a mathematical representation of an observable quantity in quantum mechanics that changes over time. It is used to describe how the state of a system evolves as time progresses.
In quantum mechanics, the act of "viewing" or observing a time-dependent Heisenberg operator does not necessarily involve physically measuring it. Instead, it refers to the process of calculating the expected value of the operator in a given state of the system.
Understanding how to "view" a time-dependent Heisenberg operator is crucial in quantum mechanics as it allows us to make predictions about the behavior of a system over time. It also helps us to better understand the fundamental principles of quantum mechanics, such as the uncertainty principle.
The expected value of a time-dependent Heisenberg operator is calculated by taking the inner product of the state vector and the operator, and then multiplying it by the conjugate transpose of the state vector. This can be represented mathematically as <ψ|A(t)|ψ>, where ψ is the state vector and A(t) is the time-dependent Heisenberg operator.
Yes, the expected value of a time-dependent Heisenberg operator can change over time as the state of the system changes. This reflects the probabilistic nature of quantum mechanics, where the expected value of an observable quantity can vary depending on the state of the system.