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". | ||
− | [[Cueball]] is standing in front of a board delivering a lesson, and is about to multiply a wavefunction by its complex conjugate. A {{w|wave function}} is a mathematical description of a quantum system which uses {{w|complex number|complex}} values - numbers that have both a {{w|real number|real}} part and an {{w|imaginary number|imaginary}} part | + | [[Cueball]] is standing in front of a board delivering a lesson, and is about to multiply a wavefunction by its complex conjugate. A {{w|wave function}} is a mathematical description of a quantum system which uses {{w|complex number|complex}} values - numbers that have both a {{w|real number|real}} part and an {{w|imaginary number|imaginary}} part. |
− | 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 | + | Complex numbers can be written in the form <math>a + bi</math>, where <math>a</math> is the real part and <math>bi</math> is the imaginary part. <math>i</math> is the imaginary unit, defined to be the square root of <math>-1</math>. |
− | + | 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 <math>a - bi</math>. | |
− | + | Multiplying the complex number by its own complex conjugate therefore yields <math>(a + bi)(a - bi)</math>. If you multiply out the brackets, you get <math>a^2 + abi - abi - b^2i^2</math>. The <math>abi</math> cancel each other out, and because <math>i = \sqrt{-1}</math>, this means that <math>i^2</math> is simply <math>-1</math>. | |
− | 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> | + | Thus, the result is <math>a^2 + b^2</math>; the imaginary part has completely disappeared, leaving nothing but a real number, so "shit has got real" as Cueball promised. |
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+ | 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. As complex numbers are often used for calculations, while more seldom finding real life applications, it is not uncommon that towards the solution of a problem, their imaginary parts are dropped again. | ||
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+ | 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> | ||
==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]] |