Harmonic Oscillator: Energy Levels Explained

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Homework Help Overview

The discussion revolves around the energy levels of the quantum harmonic oscillator, specifically the expression En=(N+1/2)hf. Participants explore the derivation and understanding of this formula in the context of quantum mechanics.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the derivation of the energy levels, with some noting that it is not found in their textbooks. There are mentions of different methods for deriving the expression, including the Power Series Technique and the use of raising and lowering operators.

Discussion Status

The discussion is ongoing, with participants sharing insights about the derivation methods. Some have expressed gratitude for the information shared, indicating a collaborative atmosphere. However, there is no explicit consensus on the preferred method of derivation.

Contextual Notes

One participant notes that the derivation is lengthy and not straightforward, which may influence the discussion's direction. There is also a mention of a lack of textbook resources on the topic, which may affect participants' understanding.

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why is the energy levels of the harmonic oscillator En=(N+1/2)hf?
 
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Is it derived in your textbook? It's not a particulary short derivation regardless of the method you use do I'd rather not type it out here. As for why the energy levels are like that because that's what you get when you solve Schrödinger's equation for a potential of the harmonic oscillator form.
 
no it's not derived in my textbook... thank you~
 
That expression for E arises when solving the Schroedinger Equation analytically using the Power Series Technique (I don't know of any other analytical technique - if anyone else does let me know).
The solution is not hard but it is long.

An easier way to derive E is to use raising and lowering operators.
 
thank you very much! :)
 

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