- #1
asdf1
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why for that equation does alpha= 2E/(hf)?
Alpha in the schrodinger's equation for the harmonic oscillator
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SUMMARY
The discussion centers on the substitution of alpha in the Schrödinger equation for the harmonic oscillator, specifically the equation psi'' + (2m/H^2)(E - 0.5kx^2)psi = 0. The variable alpha is defined as alpha = 2E/(hf), which simplifies the equation to psi'' + (alpha - y^2) = 0. Participants express curiosity about the rationale behind this substitution and suggest that alternative substitutions, such as y = (2m/H^2)E, may also be valid. The conversation emphasizes the flexibility in solving differential equations in quantum mechanics.
PREREQUISITES- Understanding of quantum mechanics principles, particularly the Schrödinger equation.
- Familiarity with harmonic oscillators in physics.
- Knowledge of energy quantization and its relation to wave functions.
- Basic mathematical skills in solving differential equations.
- Research the derivation of the Schrödinger equation for harmonic oscillators.
- Study the implications of energy quantization in quantum mechanics.
- Explore alternative methods for solving differential equations in physics.
- Learn about the role of substitutions in simplifying complex equations.
Students of quantum mechanics, physicists working with harmonic oscillators, and anyone interested in the mathematical techniques used in solving differential equations in physics.
- #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.
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- #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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