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5. [0/1 Points] DETAILS PREVIOUS ANSWERS SPH.21 The z-direction angular momentum operator in quantum mechanics is given as (SPH eqn 44): $L_z = -i\hbar \frac{\partial}{\partial \phi}$ Using this expression, and the definition of the spherical harmonics $Y_m^n(\theta, \phi)$, satisfy yourself that they are eigenfunctions of $L_z$. What is the eigenvalue of a spherical harmonic $Y_m^n(\theta, \phi)$, under the operator $L_z$, in terms of $n$, $m$, $\hbar$? $m\hbar$ Note: Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite usefull If you need $\hbar$, you can enter it into the answer box by typing 'hbar'. Do not enter a numeric value for it. Remember multiplication of two variables can either be written by using a space or by using * or \times or \cdot will give you x times y. Note that this is

          5. [0/1 Points] DETAILS PREVIOUS ANSWERS
SPH.21
The z-direction angular momentum operator in quantum mechanics is given as (SPH eqn 44):
$L_z = -i\hbar \frac{\partial}{\partial \phi}$
Using this expression, and the definition of the spherical harmonics $Y_m^n(\theta, \phi)$, satisfy yourself that they are eigenfunctions of $L_z$.
What is the eigenvalue of a spherical harmonic $Y_m^n(\theta, \phi)$, under the operator $L_z$, in terms of $n$, $m$, $\hbar$?
$m\hbar$
Note:
Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite usefull
If you need $\hbar$, you can enter it into the answer box by typing 'hbar'. Do not enter a numeric value for it.
Remember multiplication of two variables can either be written by using a space or by using * or \times or \cdot will give you x times y. Note that this is

5. [0/1 Points] DETAILS PREVIOUS ANSWERS
SPH.21
The z-direction angular momentum operator in quantum mechanics is given as (SPH eqn 44):
Lz = -iħ(∂)/(∂ϕ)
Using this expression, and the definition of the spherical harmonics Ym^n(θ, ϕ), satisfy yourself that they are eigenfunctions of Lz.
What is the eigenvalue of a spherical harmonic Ym^n(θ, ϕ), under the operator Lz, in terms of n, m, ħ?
mħ
Note:
Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite usefull
If you need ħ, you can enter it into the answer box by typing 'hbar'. Do not enter a numeric value for it.
Remember multiplication of two variables can either be written by using a space or by using * or ×or ·will give you x times y. Note that this is

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