Quantum numbers - Total Energy and Orbital Momentum

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Discussion Overview

The discussion revolves around calculating total energy, the square of the orbital momentum, and the z-component of the orbital angular momentum using specific quantum numbers (l=1, n=2, m=-1). The context includes both theoretical understanding and practical application of quantum mechanics concepts, particularly in relation to atomic physics.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant seeks assistance in calculating total energy E, L2, and Lz based on given quantum numbers.
  • Another participant questions whether the inquiry is a homework problem and suggests moving it to the appropriate section if so.
  • A participant clarifies that their inquiry is not homework-related but rather for personal study, expressing uncertainty about how to begin the calculations.
  • A later reply provides formulas for energy and angular momentum, specifically for a hydrogen atom, and mentions adjustments for other atoms.
  • Another participant offers a resource link for finding relevant formulas and suggests posting in the homework forum if the participant has specific issues with calculations.
  • One participant expresses gratitude for the provided information and indicates a plan to revisit Schrödinger's equation.

Areas of Agreement / Disagreement

Participants generally agree on the need for formulas to solve the problem, but there is no consensus on whether the inquiry should be categorized as homework or personal study. The discussion remains unresolved regarding the best approach to calculate the requested values.

Contextual Notes

The discussion includes references to specific formulas and concepts from quantum mechanics, but it does not resolve the underlying assumptions or the complexity of applying these formulas to different atomic systems.

klw289
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With the quantum numbers l=1, n=2 and m=-1 how do I calculate the total energy E, L2 (the square of the orbital momentum) and Lz (the z-component of the orbital angular momentum.

I've been trying for two hours and am getting no were. Please help
 
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klw289 said:
With the quantum numbers l=1, n=2 and m=-1 how do I calculate the total energy E, L2 (the square of the orbital momentum) and Lz (the z-component of the orbital angular momentum.

I've been trying for two hours and am getting no were. Please help

Is this a homework problem? If so, it should be moved to the homework section, and should be put in the proper homework problem format.
 
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This was not "homework" I am just reading a physics book for my own enjoyment and I was reading a section and I have no clue how to get started. I could post it in homework if its more suitable?
 
klw289 said:
This was not "homework" I am just reading a physics book for my own enjoyment and I was reading a section and I have no clue how to get started. I could post it in homework if its more suitable?

Well, the actual way that these things are figured out is to start with Schrödinger's equation. That's a pretty complicated undertaking, which can't really be described in a post. If you just want to skip to the answers: For a hydrogen atom,

E = \frac{- m q^4}{\hbar^2 n^2}

where m is the mass of an electron, q is the charge of an electron (in CSU units), n is the principal quantum number, and \hbar is Planck's constant.

L = \sqrt{l(l+1)} \hbar
L_z = m \hbar

For an atom other than a hydrogen atom, replace q^4 by N^2q^4, where N is the number of protons in the atom.
 
We consider this to be a "homework-like" problem. If your trouble is that you can't find the appropriate formulas, try here:

http://hyperphysics.phy-astr.gsu.edu/hbase/qunoh.html

Follow the links for "Principal quantum number", etc.

If you have the formulas but you can't get the numbers to come out right, go to the Introductory Physics Homework forum:

https://www.physicsforums.com/forums/introductory-physics-homework.153/

Post what you've done (show your work), and someone can probably find your mistake.

(stevendaryl slipped in ahead of me)
 
Thank you, that can get me started. I'll also go back to schrodingers equation.
 

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