# Bohr's electronic theory vs. Schroedinger equation?

1. May 9, 2006

### loom91

Hi,

I was wondering, if the Schroedinger equation implies a continuous evolution of the state vector, then how does Bohr's theory of electron's discontinuous jumps between energy states fit in? Conversely, if an electron 'jumps' from one state to another with nothing intermediate, then how can its wave-function undergo continuous evolution? Thanks.

Molu

2. May 9, 2006

### marlon

Hi,

First of all, you cannot compare the validity of Bohr's theory with that of Schroder since the first one is partly incorrect. To see why, check out our FAQ (the first post to be exact : Why Don’t Electrons Crash Into The Nucleus In Atoms?) where we have answered this question.

Enjoy

regards
marlon

3. May 9, 2006

### loom91

Yes, Bohr's concept of discreet orbits have been superceded by wavefunctions. But energy and angular momentum is still quantised, no? Their evolution is discontinuous? How does this fit into continuous unitary evolution?

Molu

4. May 9, 2006

### Staff: Mentor

No, their evolution is not discontinuous. You can model a transition between two energy levels by constructing a linear superposition of the two time-dependent wave functions, in which the coefficients are time dependent:

[tex]\Psi(x,t) = a_1(t) \Psi_1(x,t) + a_2(t) \Psi_2(x,t)[/itex]

If the wave functions are normalized properly, then at any time, $a_1^*a_1$ gives the probability that the system is in state 1, with energy $E_1$; and $a_2^*a_2$ gives the probability that the system is in state 2, with energy $E_2$.

Before the transition begins, $a_1 = 1$ and $a_2 = 0$. At some later time, after the transition has finished, $a_1 = 0$ and $a_2 = 1$.

During the transition, both $a_1$ and $a_2$ are nonzero, and the system does not have a definite energy. If you measure the energy partway through the transition, you may get either $E_1$ or $E_2$. During the transition, the probability distribution $\Psi^* \Psi$ oscillates (sloshes around or pulsates) with frequency $f = (E_2 - E_1) / h$.

Last edited: May 9, 2006
5. May 10, 2006

### loom91

Thank you, I think I understand. The wavefunction itself evolves continuously, but as measurement collapses the wavefunction, thus observations will seem to indicate discreet jumps. This is another manifestation of the measurement problem, a transition from the quantum world to the classical one.

6. May 10, 2006