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asdf1
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why for that equation does alpha= 2E/(hf)?
asdf1 said:but i think that it should make the subsitution y= (2m/H^2)E
The alpha term in the Schrodinger's equation for the harmonic oscillator represents the strength of the restoring force that brings the oscillator back to its equilibrium position. It is a measure of the stiffness or rigidity of the oscillator's potential energy function.
Changing the value of alpha in the Schrodinger's equation for the harmonic oscillator will change the frequency and amplitude of the oscillator's motion. A larger alpha value will result in a stiffer oscillator with a higher frequency and smaller amplitude, while a smaller alpha value will result in a more flexible oscillator with a lower frequency and larger amplitude.
The alpha term in the Schrodinger's equation for the harmonic oscillator is typically considered to be constant, as it represents the inherent properties of the oscillator. However, there are cases where the alpha term may change over time, such as when the oscillator is subject to external forces or when the potential energy function is not purely harmonic.
The alpha term is directly related to the energy levels of the harmonic oscillator. It determines the spacing between adjacent energy levels, with a larger alpha value resulting in a larger energy spacing between levels. This can be seen from the solution to the Schrodinger's equation, which shows that the energy levels are proportional to (n+1/2) multiplied by the square root of the alpha term.
No, the alpha term in the Schrodinger's equation for the harmonic oscillator must be positive. This is because a negative alpha value would result in an upside-down potential energy function, which is not physically realistic. Furthermore, the solution to the Schrodinger's equation would result in imaginary energy levels, which have no physical interpretation.