# Can someone help me with expectation values for the radial wavefunction?

• cwhitis
In summary, expectation values for the radial wavefunction are a way to measure the average value of a physical quantity for a given quantum state. To calculate them, the square of the wavefunction is multiplied by the variable in question and then integrated over all possible values. These values can change over time and are used in practical applications such as predicting particle behavior and understanding the properties of atoms and molecules.
cwhitis
Show that the expectation value of Lz is -2h for the radial wavefunction Y2,-2. ? Can someone do this?

Use the matrix representation for the basis l=2.

Remember that
$$\mathbf{L_z} = m\hbar$$

Last edited:
Thanks but I still don't understand, could you work it out?

That's not how it works here. It's against the forum rules to provide solutions, and you need to show some attempt at solving the problem before you'll get help here.

The wavefunction is normalized. Radial function cannot be Y, that's the spherical harmonics. Just apply the expected value in the ket-bra notation

## 1. What are expectation values for the radial wavefunction?

Expectation values for the radial wavefunction are a way to measure the average value of a physical quantity, such as energy or position, for a given quantum state. It is calculated by integrating the square of the wavefunction over all possible values of the variable in question.

## 2. How do you calculate expectation values for the radial wavefunction?

The calculation of expectation values for the radial wavefunction involves taking the square of the wavefunction and multiplying it by the variable in question, then integrating over all possible values of the variable. This can be represented mathematically as <Ψ(r)>Ψ(r) * r dr.

## 3. What is the significance of expectation values for the radial wavefunction?

Expectation values for the radial wavefunction provide valuable information about the properties of a quantum system. For example, the expectation value of energy can indicate the stability of an atom or molecule, while the expectation value of position can give insight into the location of an electron in an atom.

## 4. Can expectation values for the radial wavefunction change over time?

Yes, expectation values for the radial wavefunction can change over time as the quantum state of a system evolves. This is because the wavefunction itself can change over time, leading to different results for the expectation values.

## 5. How are expectation values for the radial wavefunction used in practical applications?

Expectation values for the radial wavefunction are used in a variety of practical applications, particularly in the field of quantum mechanics. They can help predict the behavior of particles in a system, aid in the design of new materials, and provide insight into the properties of atoms and molecules.

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