Hi there,(adsbygoogle = window.adsbygoogle || []).push({});

Once again I find myself twiddling around with some quantum mechanics, and I bumped into something I find strange. I can't see what the error of my thinking is, so I hope someone could be able to point it out.

I'm looking at solutions to the infinite square well, and arrive at the simple differential equation

[tex] \frac{d^2\Psi}{dx^2} = -k^2 \Psi [/tex]

The solution to this can be written in terms of complex exponentials or sines and cosines. I bumped into the wierd stuff when I use complex exponentials.

So the general solution in that case would be

##\Psi(x) = Ae^{ikx}+Be^{-ikx}##

Now, what I then started thinking was: "Hmmm... This could be viewed mathematically as a sum of two vectors, and solution is simply another vector."

So I drew this picture to illustrate the idea:

So from that perspective it seems that the solution could also be written as

##\Psi(x) = Ce^{ik'x}##

However, using the simple constraints of the infinite square well quickly leads to problems - namely:

##|\Psi(0)|^2 = 0##

##C = 0##

So.... Now really what I had hoped for. Where am I going taking a wrong turn? Has it to do with the x? That x should be x' also?

Thanks in advance :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mathematical conundrum when adding complex exponentials

Loading...

Similar Threads for Mathematical conundrum adding |
---|

A Can disjoint states be relevant for the same quantum system? |

A Did nature or physicists invent the renormalization group? |

A States in usual QM/QFT and in the algebraic approach |

Insights Mathematical Quantum Field Theory - Renormalization - Comments |

Insights Mathematical Quantum Field Theory - Interacting Quantum Fields - Comments |

**Physics Forums | Science Articles, Homework Help, Discussion**