Integrating the Expectation Value

In summary, the purpose of integrating the expectation value is to calculate the average value of a physical quantity in a quantum mechanical system. This value provides important insights and is calculated by taking the integral of the product of the wave function and the operator corresponding to the physical quantity. The expectation value is significant as it represents the most probable value and can be used to make predictions about the behavior of the system. It can be negative, indicating a higher probability of a negative value, and is affected by the accuracy and precision of the wave function.
  • #1
chill_factor
903
5
I am asked a problem where I'm supposed to integrate the expectation value of a dynamic variable (operator) to solve a differential equation. OK, is the expectation value supposed to be a variable?

But it seems to me like its a definite integral over allspace and thus is a number. So integrating it would just be like integrating a constant.

What does this operation of integrating the expectation value of an operator even mean conceptually?
 
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  • #2
You should write down the problem and the equations; it's not clear for me what you are talking about.
 

Related to Integrating the Expectation Value

What is the purpose of integrating the expectation value?

The purpose of integrating the expectation value is to calculate the average value of a physical quantity in a quantum mechanical system. This value can provide important insights into the behavior of the system and is often used in calculations and experiments.

How is the expectation value calculated?

The expectation value is calculated by taking the integral of the product of the wave function and the operator corresponding to the physical quantity of interest. This integral is then divided by the integral of the square of the wave function.

What is the significance of the expectation value in quantum mechanics?

The expectation value is significant because it represents the most probable value of a physical quantity in a quantum mechanical system. It also provides information about the distribution of possible values and can be used to make predictions about the behavior of the system.

Can the expectation value be negative?

Yes, the expectation value can be negative. This indicates that the system has a higher probability of having a negative value for the physical quantity being measured. It is important to note that the expectation value is not always equal to the actual measured value, but rather represents the average value of a large number of measurements.

How does the wave function affect the expectation value?

The wave function has a direct impact on the expectation value as it is used in the calculation of the integral. A more accurate and precise wave function will result in a more accurate and precise expectation value. Different wave functions can also result in different expectation values, providing insight into the behavior of the system.

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