Skip to main content
Physics

Return to Question

added 8 characters in body; edited tags; edited title
Source Link
Qmechanic ♦
Qmechanic ♦
  • 213k
  • 48
  • 590
  • 2.3k

Why do you use $n_r = n -l\ell -1$ as quantum number instead of $n$ for hydrogen atom?

I got two different quantum numbers for the same problem: Hydrogen atom without any interaction.

Then, my energy is $$ E_n = -\frac{R_y}{n^2} $$ with the quantum number $n = 1, 2, 3, ....$

In another version it is $$ E_{n_r} = -\frac{R_y}{(n_r+l+1)^2} $$$$ E_{n_r} = -\frac{R_y}{(n_r+\ell+1)^2} $$ with the quantum number $n_r = n - l -1$$$n_r = n - \ell -1$.

Unfortunately, there is no explanation why it uses $n_r$ in the second formula and what the difference physically is between $n$ and $n_r$. I guess the index stands for the quantum number due to the radial part of the wave function $R_{nl}$$R_{n\ell}$ but I am confused because it works totally fine with $n$.

Is there any explanation written somewhere or can anybody explain?

Why do you use $n_r = n -l -1$ as quantum number instead of $n$ for hydrogen atom?

I got two different quantum numbers for the same problem: Hydrogen atom without any interaction.

Then, my energy is $$ E_n = -\frac{R_y}{n^2} $$ with the quantum number $n = 1, 2, 3, ....$

In another version it is $$ E_{n_r} = -\frac{R_y}{(n_r+l+1)^2} $$ with the quantum number $n_r = n - l -1$$.

Unfortunately, there is no explanation why it uses $n_r$ in the second formula and what the difference physically is between $n$ and $n_r$. I guess the index stands for the quantum number due to the radial part of the wave function $R_{nl}$ but I am confused because it works totally fine with $n$.

Is there any explanation written somewhere or can anybody explain?

Why do you use $n_r = n -\ell -1$ as quantum number instead of $n$ for hydrogen atom?

I got two different quantum numbers for the same problem: Hydrogen atom without any interaction.

Then, my energy is $$ E_n = -\frac{R_y}{n^2} $$ with the quantum number $n = 1, 2, 3, ....$

In another version it is $$ E_{n_r} = -\frac{R_y}{(n_r+\ell+1)^2} $$ with the quantum number $n_r = n - \ell -1$.

Unfortunately, there is no explanation why it uses $n_r$ in the second formula and what the difference physically is between $n$ and $n_r$. I guess the index stands for the quantum number due to the radial part of the wave function $R_{n\ell}$ but I am confused because it works totally fine with $n$.

Is there any explanation written somewhere or can anybody explain?

Source Link
Lie
Lie
  • 112
  • 14

Why do you use $n_r = n -l -1$ as quantum number instead of $n$ for hydrogen atom?

I got two different quantum numbers for the same problem: Hydrogen atom without any interaction.

Then, my energy is $$ E_n = -\frac{R_y}{n^2} $$ with the quantum number $n = 1, 2, 3, ....$

In another version it is $$ E_{n_r} = -\frac{R_y}{(n_r+l+1)^2} $$ with the quantum number $n_r = n - l -1$$.

Unfortunately, there is no explanation why it uses $n_r$ in the second formula and what the difference physically is between $n$ and $n_r$. I guess the index stands for the quantum number due to the radial part of the wave function $R_{nl}$ but I am confused because it works totally fine with $n$.

Is there any explanation written somewhere or can anybody explain?