hokhani's latest activity
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H##Y^m_l## is a function of two variables that has complex values on a sphere. Following @WernerQH in post #6, ##p_z## is described by...
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Hhokhani replied to the thread I Visual depiction of atomic orbitals.As you clearly outlined, ##\gamma_l^m## has complex values on a sphere. In the case of ##p_z## there is no problem because ##\gamma## is...
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HThose look like the real and imaginary parts of the spherical harmonic.
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HWavefunctions are usually written down in a coordinate system where the z-axis is singled out, i.e. the azimuthal quantum number ## m ##...
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Hhokhani replied to the thread I Visual depiction of atomic orbitals.The Spherical harmonics are in the form ##\gamma_l^{m}(\theta, \phi) \propto P_l^{m}(cos \theta) e^{im\phi}##...
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Hhokhani replied to the thread I Visual depiction of atomic orbitals.I think you agree that the p-orbitals are spherical harmonics ##\gamma_l^{m}(\theta, \phi) \propto P_l^{m}(cos \theta) e^{im\phi}## with...
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Hhokhani replied to the thread I Visual depiction of atomic orbitals.Sorry, I don't know which example do you mean? As far as I understand, the spherical harmonics ##\gamma_l^{m}## are atomic orbitals...
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HThe wavefunction of an atomic orbital like ##p_x##-orbital is generally in the form ##f(\theta)e^{i\phi}## so the probability of the...
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Hhokhani reacted to JimWhoKnew's post in the thread A Angular momentum uncertainty principle and the particle on a ring with
Like.
Classically, if the ring is not in the X-Y plane then the particle's rotation is not about the Z-axis. Assuming constant ##\left|\vec... -
Hhokhani replied to the thread A Angular momentum uncertainty principle and the particle on a ring.Also in classical view, when a particle is rotating about z-axis, the x,y components of angular momentum are not zero. They are zero in...
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Hhokhani reacted to JimWhoKnew's post in the thread I Validity of identical eigenfunction of commutating operators with Like.
As @PeroK replied in #8, nothing is wrong with #7. Only basis states are considered there. But your ##\psi## in OP (#1) is a...
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Hhokhani replied to the thread I Phase and group velocity for the wave function.Please see "Solid State Physics", by Giuseppe Grosso, Giuseppe Pastori Parravicini, chapter 1, Eq. (1.71). It is interesting that in the...
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Hhokhani replied to the thread I Validity of identical eigenfunction of commutating operators.Could you please see the post #7? It approves more the discrepancy said in the post #1.
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Hhokhani replied to the thread I Validity of identical eigenfunction of commutating operators.However, in the post #1, I sent the function ##\psi=f(r,\theta) e^{im\phi}## which is always the eigenfunction of ##\hat{\mathbf{L_z}}##...
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Hhokhani reacted to JimWhoKnew's post in the thread I Validity of identical eigenfunction of commutating operators with Like.
Consider$$A=\begin{pmatrix}1&0\\0&2\end{pmatrix}$$and the identity ##2\times2## matrix ##I##...