How, and why?Stephen_G said:
The expectation value in quantum mechanics is a measure of the average value that a physical quantity will take on in a particular quantum state. It is calculated by multiplying the state's probability amplitude by the measurable quantity and then summing all possible outcomes.
Expectation value is used to predict the most probable outcome of a measurement in a particular quantum state. It also plays a crucial role in the mathematical formulation of quantum mechanics and is used to calculate important physical quantities such as energy and momentum.
No, the expectation value can never be greater than the maximum possible value of a physical quantity. This is a fundamental principle of quantum mechanics known as the uncertainty principle.
The uncertainty principle states that the more precisely one physical quantity is measured, the less precisely the conjugate quantity can be known. This means that the more accurately we know the expectation value of a physical quantity, the less we know about its exact value at any given moment.
Yes, the expectation value can be negative in certain cases. This occurs when the quantum state has a negative amplitude for a particular outcome, which cancels out the positive amplitudes of other outcomes. However, the physical interpretation of a negative expectation value is not always straightforward and requires further analysis.