Is there any reason i is left in the denominator here?

  • Thread starter Zacarias Nason
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In summary, the conversation discusses the use of continuity equations and probability current in quantum mechanics. It is noted that many of the equations have an imaginary number, i, in the denominator of the coefficient, which the individual finds confusing. They wonder why the equations are not rewritten to remove the i, as this is a common practice in physics literature. They also mention having a personal bias against leaving the i in the denominator. It is mentioned that this is a common practice for students, but not followed by professionals.
  • #1
Zacarias Nason
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I'm reading up on continuity equations and in particular how it relates to the probability current, and I noticed both in the Wikipedia page subsection for QM talking about continuity equations and in the main page for probability current, plenty of the formulas given have i in the denominator of the coefficient at the front; is there any reason the eqns are left this way rather than multiplying both sides by i^2 and then multiplying through by -1 so the LHS is still the same sign but i isn't in the denominator? Leaving the i as is is just sort of "bad voodoo" to me but functionally the same and I'm curious if there's any convention or if that's just some bias I've developed on my own.
 
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  • #2
It's one of those things students develop from drills but it is not followed by professionals. Imaginary i in the denominator is common in physics literature. Same goes for radicals / square roots.
 
  • #3
Thank you!
 

FAQ: Is there any reason i is left in the denominator here?

1. Why is "i" left in the denominator?

"i" is a mathematical symbol that represents the imaginary unit, which is defined as the square root of -1. It is often used in complex numbers and other mathematical operations. Therefore, it may be necessary to leave "i" in the denominator in order to accurately represent the solution to a problem.

2. Can "i" be simplified or cancelled out from the denominator?

In some cases, "i" can be simplified or cancelled out from the denominator. This usually occurs when the denominator contains a complex number that can be simplified or when the denominator is multiplied by its conjugate. However, it is important to carefully evaluate the problem to determine if "i" can be simplified or cancelled out without affecting the accuracy of the solution.

3. What is the purpose of "i" in the denominator?

The purpose of "i" in the denominator is to accurately represent the solution to a mathematical problem. In some cases, it may be necessary to leave "i" in the denominator in order to correctly solve a problem or to obtain a complex number as the result.

4. Can "i" be moved to the numerator?

In general, "i" cannot be moved to the numerator without affecting the accuracy of the solution. This is because "i" represents the imaginary unit and its placement in the denominator is essential to accurately represent the solution to a problem. However, there may be some cases where "i" can be moved to the numerator, such as when it is multiplied by its conjugate in the denominator.

5. Is "i" always left in the denominator in complex numbers?

No, "i" is not always left in the denominator in complex numbers. In some cases, it may be possible to simplify or cancel out "i" from the denominator. However, it is important to carefully evaluate the problem to determine if this is possible without affecting the accuracy of the solution.

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