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solas99
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In a linear superposition, what is the relationship between expectation value of, say, energy and the amplitude coefficients of the eigenfunctions?
The expectation value in a linear superposition is a way of calculating the average value of a physical quantity in a quantum system. It takes into account the probabilities of different outcomes and uses them to determine the most likely value for the quantity.
The expectation value is calculated by multiplying each possible outcome by its corresponding probability, and then summing all of these values together. Mathematically, it is represented as the inner product of the state vector and the operator representing the physical quantity.
The expectation value represents the most likely outcome for a physical quantity in a quantum system. It is not a guarantee of the actual measurement, but rather a prediction based on the probabilities of different outcomes.
When the system is measured, the expectation value may change depending on the outcome of the measurement. If the measurement corresponds to one of the possible outcomes in the superposition, then the expectation value will be equal to that outcome. Otherwise, the expectation value will be equal to zero.
The expectation value is significant because it allows us to make predictions about the most likely outcome for a physical quantity in a quantum system. It is also a fundamental concept in quantum mechanics and is used in many calculations and experiments.