Wave function simplification in relativistic coordinates?

In summary, the textbook discusses the equation ψ(x,t)=exp(i(p_{0}x^{0} + p^{→}\cdotx^{→})/h)=exp(i*p\cdotx/h), which also uses the symbol h-bar. The second equation is equivalent to the first because on the right side, p and x are considered as relativistic 4-vectors and p⋅x is the 4-vector "dot product". One person didn't initially realize this, but was reminded by another person and thanked them for the clarification.
  • #1
sciencegem
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My textbook says
ψ(x,t)=exp(i(p[itex]_{0}[/itex]x[itex]^{0}[/itex] + p[itex]^{→}[/itex][itex]\cdot[/itex]x[itex]^{→}[/itex])/h)=exp(i*p[itex]\cdot[/itex]x/h)
(note that by h I mean 'h-bar'...couldn't find the symbol).
I don't recognize (like my text implies I should) how the first equation equals the second. Where did the p[itex]_{0}[/itex]x[itex]^{0}[/itex] go? Sorry for my stupidity here. Any hints appreciated. Thanks.
 
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  • #2
On the right side, he's considering p and x as relativistic 4-vectors. p⋅x is the 4-vector "dot product" which is defined as the expression in the inner parentheses on the left side.
 
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  • #3
jtbell said:
On the right side, he's considering p and x as relativistic 4-vectors. p⋅x is the 4-vector "dot product" which is defined as the expression in the inner parentheses on the left side.

I can't believe I didn't think of that. Thank you!
 
  • #4
sciencegem said:
(note that by h I mean 'h-bar'...couldn't find the symbol).
In TeX it's \ hbar. In UTF it's just ħ
 
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  • #5
Thanks!
 

Related to Wave function simplification in relativistic coordinates?

1. What is wave function simplification in relativistic coordinates?

Wave function simplification in relativistic coordinates is a mathematical technique used to simplify the equations that describe the behavior of particles moving at high speeds, close to the speed of light. It is based on the principles of special relativity and is often used in quantum mechanics.

2. Why is wave function simplification important in relativistic coordinates?

In relativistic systems, the equations that describe the behavior of particles can become very complex and difficult to solve. Wave function simplification allows for a more manageable and accurate description of the system, making it easier to make predictions and calculations.

3. How is wave function simplification achieved in relativistic coordinates?

Wave function simplification is achieved by using mathematical transformations, such as Lorentz transformations, to convert the equations from their original form to a simpler form that takes into account the effects of special relativity.

4. What are the limitations of wave function simplification in relativistic coordinates?

While wave function simplification is a useful tool, it is not always possible to simplify the equations in relativistic systems. In some cases, the effects of special relativity cannot be accurately accounted for and the equations must be solved in their original form.

5. How is wave function simplification in relativistic coordinates used in scientific research?

Wave function simplification in relativistic coordinates is used in a variety of fields, including particle physics and astrophysics, to study the behavior of particles and objects moving at high speeds. It allows scientists to make predictions and calculations that would otherwise be impossible without taking into account the effects of special relativity.

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