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Is there a way to know qualitative information about energy spacing of bound state energy?

Infinite square well.

V=0 -a/2<x<a/2

V=∞ otherwise

Bound state energy E[itex]\propto[/itex] n^2

space beteween succesive energies increases at higher energy

(n+1)^2-n^2=2n+1

Harmonic Oscillator

V[itex]\propto[/itex]x^2

E[itex]\propto[/itex] n

space beteween succesive energies is the same at higher energy

n+1-n=1

Coloum potential

V[itex]\propto[/itex]x^-1

E [itex]\propto[/itex]n^-2

space beteween succesive energies decreases at higher energy

1/(n+1)^2-1/n^2=(2n+1)/n^2(n+1)^2

For instance, How about triangular well

V(x)=|x| -∞<x<∞

Does space between successive bound energies increase or decrease at higher energy?

How can I know this?

Infinite square well.

V=0 -a/2<x<a/2

V=∞ otherwise

Bound state energy E[itex]\propto[/itex] n^2

space beteween succesive energies increases at higher energy

(n+1)^2-n^2=2n+1

Harmonic Oscillator

V[itex]\propto[/itex]x^2

E[itex]\propto[/itex] n

space beteween succesive energies is the same at higher energy

n+1-n=1

Coloum potential

V[itex]\propto[/itex]x^-1

E [itex]\propto[/itex]n^-2

space beteween succesive energies decreases at higher energy

1/(n+1)^2-1/n^2=(2n+1)/n^2(n+1)^2

For instance, How about triangular well

V(x)=|x| -∞<x<∞

Does space between successive bound energies increase or decrease at higher energy?

How can I know this?

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