Wave propagation, +z or -z

[sokrates]

This is probably a silly question -- but I have been thinking about it, and I can't convince myself. So, I'd be greatly happy if you could solve my apparent "dilemma".

In electromagnetics, for sinusoidal voltages, we use the phasor notation and express a
positive traveling wave ( +Z direction) as follows:

$$E_+ = A_0 e^{-i \beta z }$$

where as in quantum mechanics a positive traveling wave (+Z direction) is written as follows (correct me if I am wrong)

$$\Psi_+ = A_0 e^{+i \beta z}$$

where beta's are wavenumbers.

Where am I messing this up?

 

[azntoon]

Why is the sign in the exponent different? The answer to your question lies in the fact that the two equations you mention represent two different physical phenomena. In electromagnetics, the equation you mention represents an electric field wave travelling in the +Z direction. On the other hand, the equation in quantum mechanics represents a wavefunction describing the behavior of a particle. The difference in the signs of the exponents can be explained by considering the phase conventions used in the two fields. In electromagnetism, the convention is to use a negative sign for the exponential term to represent a wave travelling in the +Z direction, while in quantum mechanics, the convention is to use a positive sign for the exponential term to represent a wave travelling in the +Z direction.