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==Explanation==
 
==Explanation==
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This was the second comic with one of [[Randall|Randall's]] [[:Category:Fun fact|fun facts]].
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{{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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[[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. Multiplying a wavefunction by its complex conjugate is a common thing to do, as it yields the probability density of where a particle is likely to be found, which is a real-valued function.
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[[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.
  
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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.
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Complex numbers are 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>.
  
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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 just got real" as Cueball promised.
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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>.
  
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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. 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.
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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>.
  
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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>, a {{w|Differential equation|differential equation}} that the {{w|Wavefunction|wavefunction}} Ψ, which determines the possible positions of a quantum particle over time, always satisfies. The {{w|Derivative#Partial_derivatives|derivative}} should be written with ∂Ψ on the top; the omission of the Ψ may be a mistake.
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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.
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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==
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:[Cueball, holding a marker pen down in one hand, is standing at a whiteboard with two equations, one of which is the time-dependent Schrodinger equation and the other shows what the wavefunction equals, but from there it becomes unreadable. Below is a graph with a bell-shaped curve. There are also other unreadable markings on the board below the second equation and next to the graph.]
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:[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.
  
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:[In a frame-less panel Cueball is seen writing on the whiteboard. This is seen from the side of the board, so it is just a thin line with a shelf at the bottom for putting the pen on.]
 
 
: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.
  
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:[Dramatic zoom in on Cueball appears to be writing the final part of his next equation.]
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:[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:Fun fact]]
 
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Math]]
 
[[Category:Math]]
 
[[Category:Physics]]
 
[[Category:Physics]]
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[[Category:Fun fact]]
 
[[Category:Puns]]
 
[[Category:Puns]]

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