Exploring the Complexity of Psi: A Deeper Look into this Mysterious Phenomenon

In summary, psi is complex because it is easier to write the wave function in complex numbers. It's not neccessarily complex.
  • #1
imran
18
0
why psi is complex!
why can't it is a real ? :rolleyes:
 
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  • #2
because it is easier to write the wave function in complex numbers.
 
  • #3
It's not neccessarily complex. Take the infinite square well for an example. What your hamiltonian is like determines what the wave function turns out to be. As far as I know the only restrictions on psi are that it must be a continuous, single valued function, normalizable and that it's first derivative must be continuous excluding points where the potential is infinite.
 
  • #4
imran said:
why psi is complex!
why can't it is a real ?

Because that's the only way people have figured out how to get predictions that agree with experiment.

OK, you can say it's because of the way the Schrödinger Equation is set up. Solutions to the S.E. have to be complex. But that just changes the question to "why is the Schrödinger Equation the way it is?" You can't win. :cry:

Sterj said:
because it is easier to write the wave function in complex numbers.

That's true for E&M. You can do electromagnetic waves using only real sines and cosines, but the math is easier sometimes if you use complex exponentials instead. In QM, on the other hand, you need those i's. The only way around them is to write the real and imaginary parts of psi as separate functions, and turn the Schrödinger Equation into a pair of coupled differential equations that mix the two functions together. But that just rephrases imran's question to, "why do we have to do that?" Again, you can't win. :cry:

inha said:
It's not neccessarily complex. Take the infinite square well for an example.

You're probably thinking of the time-independent stationary state wave function psi(x). Include the time dependence to make it psi(x,t) and you'll make it complex. I tried to include an example, but the TeX parser doesn't seem to be working right now... I get the equations I posted in another message over the weekend, on another subject entirely!
 
  • #5
jtbell said:
You're probably thinking of the time-independent stationary state wave function psi(x). Include the time dependence to make it psi(x,t) and you'll make it complex. I tried to include an example, but the TeX parser doesn't seem to be working right now... I get the equations I posted in another message over the weekend, on another subject entirely!

Ah yes. I should have mentioned the time independence. It seems that I type faster than it's good for me.
 
  • #6
imran said:
why psi is complex!
why can't it is a real ? :rolleyes:

If you start from the de Broglie's relations for the energy and the momentum, and you assume that they are related by the classical relation [itex] E = { {\vec p}^2 \over 2 m} + V({\vec r})[/itex], and you assume that that plane waves solutions must exist, and you assume linearity, then you are forced to introduced complex numbers. The key point is that the equation mixes a first derivative (to get the energy) and second derivatives (to get the p^2). In contrast, the classical wave equation contains only second derivatives.

Pat
 
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  • #7
nrqed said:
The key point is that the equation mixes a first derivative (to get the energy) and second derivatives (to get the p^2). In contrast, the classical wave equation contains only second derivatives.

Gee, that's smart :approve:

Patrick.
 
  • #8
NRQED, that is indeed a very nice description...one to remember

marlon
 
  • #9
If somebody of you is interested in reading what contemporary physicist thinks about the problem try www.quniverse.sk/buzek/zaujimave/p343_s.pdf[/URL] . As an attracting example let me give you a very small citation:
"But what of psi (r) itself? Why is it a complex number,
composed of `real’ and `imaginary’ parts, Re psi(r)+ i I am psi(r)?
The surprising truth, I believe, is that at this point we do
not know why psi has two parts."
 
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1. Why is the concept of Psi Complex important in the field of science?

The Psi Complex, also known as the Psi phenomenon, is a term used to describe the supposed ability of the mind to affect matter or interact with the physical world through extrasensory means. It is important in the field of science because it challenges our understanding of the mind and its capabilities, and has the potential to revolutionize our understanding of consciousness and the nature of reality.

2. Is there any scientific evidence to support the existence of Psi Complex?

While there have been numerous studies and experiments conducted on the subject, there is currently no conclusive scientific evidence to support the existence of Psi Complex. Some studies have shown promising results, but they have not been able to withstand rigorous scientific scrutiny. Therefore, the concept of Psi Complex remains a controversial and debated topic in the scientific community.

3. How does Psi Complex differ from other forms of psychic abilities?

Psi Complex is often used as an umbrella term for a variety of psychic abilities, including telepathy, clairvoyance, and psychokinesis. However, the key difference is that Psi Complex involves the use of extrasensory abilities to interact with the physical world, while other forms of psychic abilities may involve communication or perception of non-physical entities or information.

4. Can anyone develop Psi Complex abilities?

There is currently no scientific evidence to suggest that anyone can develop Psi Complex abilities. Some people may claim to possess these abilities, but without scientific proof, it is difficult to determine if they are genuine or not. It is also important to note that many factors, such as belief, suggestion, and coincidence, can influence the perception of Psi Complex abilities.

5. What are the potential implications of proving the existence of Psi Complex?

If Psi Complex is ever proven to be a real phenomenon, it could have significant implications for our understanding of the human mind and consciousness. It could also have practical applications in fields such as medicine, communication, and technology. However, it is important to approach this concept with caution and continue to conduct rigorous scientific research before drawing any conclusions.

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