Complex conjugate of the expectation value of momentum

In summary, the complex conjugate of <p> is obtained by adding a minus to the i and switching the stars in eq 1.35. This can be done only under the assumption that the wavefunction is normalized to unity.
  • #1
jb646
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Homework Statement


Compute the complex conjugate of <p> using eq 1.35 (<p>=∫ψ*(h/i)∂/∂x ψ dx) and prove that <p> is real (<p>=<p>*)


Homework Equations


equation 1.35 is given above


The Attempt at a Solution


to take the c.c. don't i just add a minus to the i and switch the stars like so:
<p>=∫ψ(-h/i)∂/∂x ψ* dx
i think that is right, but it seems too simple for what i should be doing. as for the second part, could somebody please nudge me in the right direction.

thanks for all your help.
 
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  • #2
Well, now comes the tricky part, shifting the derivative under the integral back to the psi. This is done only under the assumption that the wavefunction is normalized to unity.

Can you do it now ?
 

1. What is the complex conjugate of the expectation value of momentum?

The complex conjugate of the expectation value of momentum refers to the complex conjugate of the average value of the momentum of a particle in a quantum system. It is represented by the symbol ⟨p⟩* and is calculated by taking the average of the product of the momentum operator and the wave function of the system.

2. How is the complex conjugate of the expectation value of momentum related to the uncertainty principle?

The complex conjugate of the expectation value of momentum is related to the uncertainty principle because it is used to calculate the uncertainty in the momentum of a particle in a quantum system. The uncertainty principle states that the more precisely we know the position of a particle, the less precisely we can know its momentum and vice versa. The complex conjugate of the expectation value of momentum helps us calculate this uncertainty in momentum.

3. Can the complex conjugate of the expectation value of momentum be a complex number?

Yes, the complex conjugate of the expectation value of momentum can be a complex number. This is because the expectation value of momentum is calculated using the complex-valued wave function of the system, which can result in a complex number. The complex conjugate of this value will also be a complex number.

4. How is the complex conjugate of the expectation value of momentum used in quantum mechanics?

The complex conjugate of the expectation value of momentum is an important concept in quantum mechanics as it helps us calculate the average value of the momentum of a particle in a quantum system. This value is then used in various equations and principles, such as the uncertainty principle, to understand the behavior and properties of particles at the quantum level.

5. Is the complex conjugate of the expectation value of momentum the same as the expectation value of the complex conjugate of momentum?

No, the complex conjugate of the expectation value of momentum is not the same as the expectation value of the complex conjugate of momentum. While the former refers to the average value of the momentum of a particle, the latter refers to the average value of the complex conjugate of the momentum operator. These two values are not interchangeable in quantum mechanics and have different physical interpretations.

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