Energy quantization in schrodinger equation

[suku]

in schrodinger equation(time independent)

d^2y/dx2= 2m/h^2(V-E)y, V is a function of position coordinate, y is eigenfunction.
if E>V , y being -ve or +ve it would be a oscillatory function. The allowed energy values are continously distributed. Does this region correspond to classical regime of continuous energy values?
thnks for any rply.

 

[Trolle]

The quantum particle you are describing will behave as a free quantum particle, however not necessarily as a classical particle, if that is what you are asking...?

A quantum particle doesn't exist in any particular eigenstate - it exists in a superposition of all eigenstates... Thus the idea of comparing energy eigenvalues to classical (absolute) energy values seems wrong.

If, however, the uncertainty in energy (as in the uncertainty principle) becomes negible, we can treat the energy of our particle as an absolute, and thus make an analogy to classical energy...

- Trolle

 

[Entropia]

Yes, the region where E>V corresponds to the classical regime of continuous energy values. In classical mechanics, energy is considered to be a continuous quantity and can take on any value. However, in quantum mechanics, the Schrodinger equation describes the behavior of particles at the atomic and subatomic level, where energy is quantized and can only take on specific, discrete values. This is reflected in the equation, where the energy term (E) is multiplied by the eigenfunction (y), which represents the probability amplitude of finding the particle at a certain position. The allowed energy values are determined by the boundary conditions and the potential energy function (V), and they are not continuously distributed like in classical mechanics. Therefore, the region where E>V in the Schrodinger equation corresponds to the classical regime of continuous energy values.