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pardesi
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How does this follow from the defintion of the expectation value of xGriffith said:The expectation value is the average of repeated measurements on an ensemble of identically prepared systems
How does this follow from the defintion of the expectation value of xGriffith said:The expectation value is the average of repeated measurements on an ensemble of identically prepared systems
You have it backwards.pardesi said:How does this follow from the defintion of the expectation value of x
The expectation value of x is a mathematical concept used in quantum mechanics to describe the average value of a physical quantity, such as position or momentum, in a given state of a system. It is represented by the symbol 〈x〉 and is calculated by taking the sum of the product of the possible values of x and their respective probabilities.
The expectation value of x is calculated by taking the integral of x multiplied by the probability density function, or by summing the product of the possible values of x and their respective probabilities.
The expectation value of x represents the average value of a physical quantity, such as position or momentum, in a given state of a system. It is not necessarily the actual value that will be measured, but rather the most probable value.
The expectation value of x is related to uncertainty through the Heisenberg uncertainty principle, which states that the product of the uncertainties of two complementary physical quantities, such as position and momentum, must be greater than or equal to the reduced Planck's constant divided by 2.
Yes, the expectation value of x can be negative. This indicates that there is a higher probability of the physical quantity having a negative value rather than a positive one. However, the expectation value itself is a measure of the average value and does not necessarily represent the actual value that will be measured.