- #1

- 734

- 0

## Main Question or Discussion Point

why is the lowest allowed energy not E=0 but some definite minimum E=E0?

- Thread starter asdf1
- Start date

- #1

- 734

- 0

why is the lowest allowed energy not E=0 but some definite minimum E=E0?

- #2

siddharth

Homework Helper

Gold Member

- 1,127

- 0

If you solve the Time Independent Schrodinger equation for the Harmonic Oscillator, that is

[tex] -\frac{\hbar^2}{2m} \frac{d^2\Psi}{dx^2} + \frac{1}{2}kx^2 \Psi = E \Psi [/tex]

The quantization of energy comes from the boundary conditions (ie, [itex] \Psi = 0 [/itex] when [itex] x= \infty [/itex] or [itex] x = -\infty [/itex]).

The permitted energy levels will be

[tex] E_n = (n+\frac{1}{2}) \hbar \omega [/tex]

So the lowest Energy is not E=0.

[tex] -\frac{\hbar^2}{2m} \frac{d^2\Psi}{dx^2} + \frac{1}{2}kx^2 \Psi = E \Psi [/tex]

The quantization of energy comes from the boundary conditions (ie, [itex] \Psi = 0 [/itex] when [itex] x= \infty [/itex] or [itex] x = -\infty [/itex]).

The permitted energy levels will be

[tex] E_n = (n+\frac{1}{2}) \hbar \omega [/tex]

So the lowest Energy is not E=0.

Last edited:

- #3

Galileo

Science Advisor

Homework Helper

- 1,989

- 6

If E=0 both x and v are zero, which contradicts Heisenberg.

- #4

- 734

- 0

thank you very much!!! :)

- Last Post

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 498

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 13

- Views
- 1K