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Answered how to recognize m=0
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Dr. Nate
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It's not as well-known as it should be that $p_x$ and $p_y$ are superpositions of the $m_l=\pm1$ orbitals. That means the $p_x$ and $p_y$ orbitals no longer have $m_l$ as a quantum number. This is true for most pictures you will see of other shells' $m\ne0$ orbitals. They do this so that the wave functions are purely real and easy to draw.

So when you see those three figure-eights in different orientations, those are $p_x$, $p_y$, and $p_z$. Sometimes, they don't even want to show a lobe is the negative of the other, so they show you the absolute value of the superposition.

This means that $m=0$ is always the one they label with a single $z$.

You'll know you are actually looking at sets of determinate orbitals and not superpositions if all orbitals have a continuous axial symmetry about the $z$-axis. But since they are complex, if you see these images, you might be looking at $|\Psi|^2$. Check out Griffiths or Alastair I. M. Rae. Griffiths plots $|\Psi|^2$ and tells you how to recognize them from their nodes. Rae instead plots $|\Psi|$.

It's not as well-known as it should be that $p_x$ and $p_y$ are superpositions of the $m_l=\pm1$ orbitals. That means the $p_x$ and $p_y$ orbitals no longer have $m_l$ as a quantum number. This is true for most pictures you will see of other shells' $m\ne0$ orbitals. They do this so that the wave functions are purely real and easy to draw.

So when you see those three figure-eights in different orientations, those are $p_x$, $p_y$, and $p_z$. Sometimes, they don't even want to show a lobe is the negative of the other, so they show you the absolute value of the superposition.

You'll know you are looking at determinate orbitals and not superpositions if all orbitals have a continuous axial symmetry about the $z$-axis. But since they are complex, if you see these images, you might be looking at $|\Psi|^2$. Check out Griffiths or Alastair I. M. Rae. Griffiths plots $|\Psi|^2$ and tells you how to recognize them from their nodes. Rae instead plots $|\Psi|$.

It's not as well-known as it should be that $p_x$ and $p_y$ are superpositions of the $m_l=\pm1$ orbitals. That means the $p_x$ and $p_y$ orbitals no longer have $m_l$ as a quantum number. This is true for most pictures you will see of other shells' $m\ne0$ orbitals. They do this so that the wave functions are purely real and easy to draw.

So when you see those three figure-eights in different orientations, those are $p_x$, $p_y$, and $p_z$. Sometimes, they don't even want to show a lobe is the negative of the other, so they show you the absolute value of the superposition.

This means that $m=0$ is always the one they label with a single $z$.

You'll know you are actually looking at sets of determinate orbitals and not superpositions if all orbitals have a continuous axial symmetry about the $z$-axis. But since they are complex, if you see these images, you might be looking at $|\Psi|^2$. Check out Griffiths or Alastair I. M. Rae. Griffiths plots $|\Psi|^2$ and tells you how to recognize them from their nodes. Rae instead plots $|\Psi|$.

Source Link
Dr. Nate
  • 459
  • 2
  • 10

It's not as well-known as it should be that $p_x$ and $p_y$ are superpositions of the $m_l=\pm1$ orbitals. That means the $p_x$ and $p_y$ orbitals no longer have $m_l$ as a quantum number. This is true for most pictures you will see of other shells' $m\ne0$ orbitals. They do this so that the wave functions are purely real and easy to draw.

So when you see those three figure-eights in different orientations, those are $p_x$, $p_y$, and $p_z$. Sometimes, they don't even want to show a lobe is the negative of the other, so they show you the absolute value of the superposition.

You'll know you are looking at determinate orbitals and not superpositions if all orbitals have a continuous axial symmetry about the $z$-axis. But since they are complex, if you see these images, you might be looking at $|\Psi|^2$. Check out Griffiths or Alastair I. M. Rae. Griffiths plots $|\Psi|^2$ and tells you how to recognize them from their nodes. Rae instead plots $|\Psi|$.