Why the energy eigen values for negative energies are always discrete

[ironcross77]

Why the energy eigen values for negetive energies are always discrete while that for positive energies are always continuous?

Also what is oscillation theorem?

 

[qtp]

the energy eigen values for positive energies isn't always continuous as far as i know from QM. and oscillation theorem is at the heart of physics and says that everything in the physical world can be known by a harmonic oscillator lol j/k but they try to make it work anyway