- #1
asdf1
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why for that equation does alpha= 2E/(hf)?
Alpha in the schrodinger's equation for the harmonic oscillator
- Thread starter asdf1
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Homework Help Overview
The discussion revolves around the Schrödinger equation for the harmonic oscillator, specifically focusing on the parameter alpha and its definition in relation to energy. Participants are exploring the implications of different substitutions in the equation.
Discussion Character
- Exploratory, Conceptual clarification, Problem interpretation
Approaches and Questions Raised
- Participants are questioning the definition and role of alpha in the equation, with some suggesting it may be a simplification for notation. There is also a discussion about alternative substitutions and their potential effectiveness.
Discussion Status
The conversation is ongoing, with participants sharing their interpretations and questioning the textbook's approach. Some guidance has been offered regarding the flexibility of substitutions in solving the equation, but no consensus has been reached on the best approach.
Contextual Notes
There is a noted lack of clarity regarding the definition of alpha, which is impacting the discussion. Additionally, the original poster's uncertainty about the textbook's substitution is a point of interest.
- #2
Galileo
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Since you haven't mentioned what alpha is supposed to represent, how are we to supposed to answer that question? I can't read minds you know. Alpha is not an agreed upon universal variable.
To me it sounds like a definition. There to simplify notation.
It is equal to the ration of the energy to the ground state energy.
To me it sounds like a definition. There to simplify notation.
It is equal to the ration of the energy to the ground state energy.
Last edited:
- #3
asdf1
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sorry for being unclear~
psi`` + (2m/H^2)(E-0.5kx^2)psi=0
my textbook says that to simply that equation, it makes the subsitution
alpha= 2E/(hf) so that
psi``+(alpha-y^2)=0
but i think that it should make the subsitution y= (2m/H^2)E
psi`` + (2m/H^2)(E-0.5kx^2)psi=0
my textbook says that to simply that equation, it makes the subsitution
alpha= 2E/(hf) so that
psi``+(alpha-y^2)=0
but i think that it should make the subsitution y= (2m/H^2)E
- #4
jtbell
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asdf1 said:
So go ahead and try it and see if it helps better than the other substitution! It's certainly possible that it might work. There's usually more than one way to skin a cat (or solve an equation), after all.
- #5
asdf1
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you're right~ :)
just curious why the book made that substituition, though~
just curious why the book made that substituition, though~
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