Modern Physics: Chapter 7 – Introduction to Wavefunctions


So I already mentioned that everything has a matter-wave associated with it. Developing the idea a bit further, we get the concept of a wavefunction which, by convention, is denoted by \psi.

Each physical system is described by a state function which determines all can be known about the system. … The wavefunction has to be finite and single valued throughout position space, and furthermore, it must also be a continuous and continuously differentiable function.

– Derivation of the postulates of quantum mechanics from the first principles of scale relativity

Furthermore, a wavefunction is generally a complex function i.e it consists of both a real part and an imaginary part.

  • \psi (x, t) – A wavefunction

To get the probably of a particle being at a position x, you have to get a real value out of the complex wavefunction. Hence the probably of finding a particle described by a wavefunction \psi is the product of the function \psi at x and its complex conjugate \psi^{*} at x.

  • \psi (x_{0}) \psi^{*}(x_{0}) – probability of finding the particle at x_{0}.

To get the probability from a range x \in (x_{0}, x_{1}) where x is a continous variable, you can take the integral of \psi^{*}\psi from x_{0} to x_{1}:

  • P(x) = \int_{x_{0}}^{x_{1}} \psi^{*}(x) \psi(x) dx

How to Win an Internet Argument


Credits: XKCD [ http://xkcd.com/386/ ]

Choose the Right Viewpoint

Before taking part in an online argument, it is wise to carefully choose a viewpoint that is the most widely believed and hence will get you the most public support. Knowing which viewpoint is supported by the majority of the population is easy: just pick the one that is stupidest, requires the least amount of intelligence, is supported by the most politicians and has the least amount of evidence to back it up. An argument with all of these qualities is guaranteed to be the one with the most public support.

Wrong: Climate Change is a major challenge for our species and we need to use all our combined intellect and resources to avert this catastrophe and leave a better world for future generations.

Right: Climate Change is false propaganda by those pesky liberals.

Awesome: Climate Change is a conspiracy by the Illuminati so they can control the world and impose evil things like science and education on the innocent population.

Use Incorrect Grammar

Whatever you do, don’t write a single sentence that is actually comprehensible.  Using correct grammar or language that suggests you were privileged enough to receive even the most minimal amount of education  is suicide in the world of online arguments. It is also extremely crucial that you misspell all words that are more than three letters long.

Wrong: I am sorry sir, but you seem to be exceedingly ignorant and uninformed of the issue at hand.

Right: Die u stupid imbaceele!

Awesome: Fak u fegit, K? U bez stoopid. Plz dying now.

Credits: XKCD [ http://xkcd.com/1081/ ]

Take Ad Hominem to the Next Level

Whoever said nonsense like, “Attack the idea, not the person“, was clearly an Indian agent trying to spread false propaganda. To win an internet argument you must never ever ever pay attention to the your opponent’s ideas, logic or evidence. The best thing to do is to disregard everything he has to say and keep hurling insults at him, his parents and (only for professionals) his ancestry, race and language.

Preposterously Wrong: I agree with most of your evidence however you must remember that correlation does not imply causation in all cases, and hence the conclusions you draw may be unjustified.

Wrong: Your argument is invalid.

Right: Damn u aNd ur grAndMa. U <insert race> morons r <insert unfriendly country> agents trys 2 destroying my contry. Pplz like u shud B deadened and hanging. Stoopid treitor pPlz.

The Capslock is Your Friend

You may sometimes run into a problem if your assertion is not convincing enough. Some people make the mistake of mentioning objective evidence and logic to support their claim. That’s stupid, don’t do that. The best technique to work your way out of this situation is to  just keep repeating your assertion in an exceedingly aggressive and illiterate-sounding tone. Turning on the caps-lock and SHOUTING EVERYTHING IN CAPS!!!!!!!!!!!!!!!!!!!!!  is strongly recommended.

And that’s that. I’m sure with these simple, easily implementable techniques you will never lose an internet argument again.