Editing 849: Complex Conjugate
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==Explanation== | ==Explanation== | ||
− | + | {{incomplete|The Schrodinger wave equation needs explaining.}} | |
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". | 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". | ||
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Complex numbers can be written in the form a + bi, where a is the real part and bi is the imaginary part. i is the imaginary unit, defined so that i² = -1. The {{w|complex conjugate}} of a complex number simply reverses the sign on the imaginary part - so for the number above, the complex conjugate is a - bi. | Complex numbers can be written in the form a + bi, where a is the real part and bi is the imaginary part. i is the imaginary unit, defined so that i² = -1. The {{w|complex conjugate}} of a complex number simply reverses the sign on the imaginary part - so for the number above, the complex conjugate is a - bi. | ||
− | Multiplying the complex number by its own complex conjugate therefore yields (a + bi)(a - bi). If you multiply out the brackets, you get a² + abi - abi - b²i². The abi cancel each other out, and i² can be replaced by -1. Thus, the result is a² + b², a real number, so "shit | + | Multiplying the complex number by its own complex conjugate therefore yields (a + bi)(a - bi). If you multiply out the brackets, you get a² + abi - abi - b²i². The abi cancel each other out, and i² can be replaced by -1. Thus, the result is a² + b², 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. Because nonreal numbers are often considered to have no physical significance, turning them into real numbers to produce a final answer is so common that this joke would quickly become tedious. | 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. Because nonreal numbers are often considered to have no physical significance, turning them into real numbers to produce a final answer is so common that this joke would quickly become tedious. | ||
− | The wave function shown on Cueball's board is the {{w|Schrödinger_equation|time-dependent Schrödinger equation}} <math>i\hbar\dfrac{\partial}{\partial t} = \hat{H}\Psi</math>, a {{w| | + | The wave function shown on Cueball's board is the {{w|Schrödinger_equation|time-dependent Schrödinger equation}} <math>i\hbar\dfrac{\partial}{\partial t} = \hat{H}\Psi</math>, a {{w|differential equation|differential equation}} that the {{w|wavefunction|wavefunction}} Ψ always satisfies. The {{w|derivative|partial derivative}} should be written with ∂Ψ on the top; the omission of the Ψ may be a mistake. |
==Transcript== | ==Transcript== | ||
− | :[Cueball | + | :[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: 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: Because I'm multiplying the wavefunction by its complex conjugate. | ||
:Cueball: That's right. | :Cueball: That's right. | ||
− | :[Dramatic zoom | + | :[Dramatic zoom. It appears Cueball is writing on the side of the panel.] |
:Cueball: Shit just got ''real''. | :Cueball: Shit just got ''real''. | ||
{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||
[[Category:Math]] | [[Category:Math]] | ||
[[Category:Physics]] | [[Category:Physics]] | ||
+ | [[Category:Fun fact]] | ||
[[Category:Puns]] | [[Category:Puns]] |