849: Complex Conjugate
Title text: Fun fact: if you say this every time a professor does something to a complex-number equation that drops the imaginary part, they'll eventually move the class to another room and tell everyone else except you.
| This explanation may be incomplete or incorrect: The Schrodinger wave equation needs explaining.|
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This comic is a joke on the phrase "Shit just got real", which means "something has suddenly increased in difficulty and become genuinely challenging or dangerous".
Cueball is standing in front of a board delivering a lesson, and is about to multiply a wavefunction by its complex conjugate. A wave function is a mathematical description of a quantum system which uses complex values - numbers that have both a real part and an imaginary part.
Complex numbers are written in the form , where is the real part and is the imaginary part. is the imaginary unit, defined to be the square root of .
The complex conjugate of a complex number simply reverses the sign on the imaginary part - so for the number above, the complex conjugate is .
Multiplying the complex number by its own complex conjugate therefore yields . If you multiply out the brackets, you get . The cancel each other out, and because , this means that is simply .
Thus, the result is ; the imaginary part has completely disappeared, leaving nothing but a real number, so "shit has got real" as Cueball promised.
The title text notes that you can make this joke in class every time a calculation is performed that drops the imaginary part from a complex number, but warns that it would be so annoying that the professor will eventually find a way to have the class without you in it.
The wave function shown on Cueball's board is the time-dependent Schrödinger equation
- [Cueball is standing at a whiteboard covered in equations, one of which is the time dependent Schrodinger equation.]
- Cueball: Okay, anyone who's feeling like they can't handle the physics here should probably just leave now.
- Cueball: Because I'm multiplying the wavefunction by its complex conjugate.
- Cueball: That's right.
- [Dramatic zoom. It appears Cueball is writing on the side of the panel.]
- Cueball: Shit just got real.
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