Wave propagation, +z or -z

In summary, the difference in the signs of the exponents in the two equations mentioned is due to the different physical phenomena they represent and the phase conventions used in each field. In electromagnetism, a negative sign is used to represent a wave travelling in the +Z direction, while in quantum mechanics, a positive sign is used for the same direction.
  • #1
sokrates
483
2
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:

[tex]E_+ = A_0 e^{-i \beta z }[/tex]

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

[tex] \Psi_+ = A_0 e^{+i \beta z} [/tex]

where beta's are wavenumbers.

Where am I messing this up?
 
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  • #2
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.
 
  • #3


Thank you for your question. It is not a silly question at all and it is important to have a clear understanding of wave propagation in both electromagnetics and quantum mechanics. The confusion may arise from the fact that in electromagnetics, the direction of wave propagation is often denoted by +z or -z, while in quantum mechanics, it is denoted by +k or -k, where k is the wave vector. However, these notations are referring to the same physical concept of the direction of wave propagation in a particular coordinate system.

In both cases, the direction of wave propagation is determined by the sign of the wavenumber (beta or k). A positive wavenumber indicates a wave propagating in the positive direction, while a negative wavenumber indicates a wave propagating in the negative direction.

In electromagnetics, the phasor notation is used to represent the amplitude and phase of a sinusoidal wave, while in quantum mechanics, the wave function (Psi) is used to describe the probability amplitude of a particle. The difference in notation is simply due to the different mathematical formalisms used in these two fields.

Therefore, there is no mistake in your understanding. You are correct in your expressions for a positive traveling wave in both electromagnetics and quantum mechanics. The only difference is in the notation used to represent the direction of wave propagation. I hope this clarifies your dilemma. Keep asking questions and seeking understanding in your scientific pursuits.
 

1. How does wave propagation differ in the +z and -z directions?

In a +z direction, the wave propagates in the positive direction along the z-axis. In a -z direction, the wave propagates in the negative direction along the z-axis. This means that the wave travels in opposite directions in +z and -z directions.

2. What factors can affect the direction of wave propagation in the +z and -z directions?

The direction of wave propagation can be affected by the medium through which the wave travels, the angle of incidence, and the frequency of the wave.

3. How does the amplitude of a wave change in the +z and -z directions?

In a +z direction, the amplitude of the wave decreases as it travels further away from its source. In a -z direction, the amplitude of the wave increases as it travels closer to its source. This is due to the spreading out and focusing of the wave, respectively.

4. Can a wave propagate in both the +z and -z directions simultaneously?

Yes, a wave can propagate in both the +z and -z directions simultaneously. This is known as bidirectional propagation and is often seen in waves that reflect off of a boundary or interface.

5. How does the speed of a wave change in the +z and -z directions?

In a homogeneous medium, the speed of the wave remains constant in both the +z and -z directions. However, in a non-homogeneous medium, the speed of the wave may change depending on the properties of the medium in each direction.

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