# Generalized Schrödinger equation

1. Jan 20, 2014

### Maximise24

This equation (see attachment) appears in one of Prof. Susskinds's lectures on Quantum Mechanics: in trying to differentiate the coefficients of the eigenvectors of a wave function with respect to time, an exponential e^(-iEt) is introduced for alpha.

I can see that d/dt e^(-iEt) = -iE e^(-iEt), but why is the second part e^(-iEt) not in the top equation in the attachment? Is it disregarded because it's just a number?

Thanks for any help provided!

2. Jan 20, 2014

### Maximise24

Attachment seems to have got lost.

#### Attached Files:

• ###### QM.jpg
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3. Jan 20, 2014

### dextercioby

But the exponential is there, disguised under the form of 'alpha' in the rhs.

4. Jan 20, 2014

### Maximise24

OK, so $\alpha$j(0)e-iEt has simply been conflated into $\alpha$j? Can you just do that since e-iEt is not a constant?
Thanks!

5. Jan 20, 2014

### dextercioby

The only variable is time. e^{-iEt} in units with hbar=1 gathers the time dependence of alpha.

6. Jan 20, 2014

### Jilang

Aj is defined on the second line of your picture. It doesn't look like a constant to me.

7. Jan 20, 2014

### Maximise24

OK, thanks guys.