Normalization said:Homework Statement
Why does the extra phase factor cancel out? Is it because you are multiplying the wave-function with the extra phase factor by its conjugate and if so, why should it matter that the extra phase factor is independent of x?
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Normalization said:
The expectation value of a dynamical variable is a mathematical concept used in quantum mechanics to describe the average value of a physical property of a quantum mechanical system. It is often denoted as <A> and is calculated by taking the inner product of the state vector with the operator corresponding to the dynamical variable.
The expectation value of a dynamical variable represents the most probable outcome of a measurement of that variable. It is also related to the uncertainty in the system, as described by Heisenberg's uncertainty principle. The larger the uncertainty in a system, the larger the spread of possible expectation values for a given dynamical variable.
Yes, the expectation value of a dynamical variable can be negative. This can occur when the state vector of the system has a complex phase, which is a common occurrence in quantum mechanics. However, the magnitude of the expectation value is still a measure of the average value of the dynamical variable.
The expectation value of a dynamical variable is a time-dependent quantity and can change over time as the state of the system evolves. This is described by the Schrödinger equation, which governs the time evolution of quantum mechanical systems.
No, the expectation value of a dynamical variable cannot be used to predict the exact outcome of a measurement. It represents the average value of the variable and does not take into account the quantum fluctuations that can occur during a measurement. These fluctuations are inherent to quantum mechanics and cannot be predicted with certainty.