A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function. It is a central entity in quantum mechanics and is important in all modern theories, like quantum field theory incorporating quantum mechanics, while its interpretation may differ. The most common symbols for a wave function are the Greek letters ψ or Ψ
The image above shows the comparison of classical and quantum harmonic oscillator conceptions for a single spinless particle. The two processes differ greatly. The classical process (A–B) is represented as the motion of a particle along a trajectory. The quantum process (C–H) has no such trajectory. Rather, it is represented as a wave. Panels (C–F) show four different standing wave solutions of the Schrödinger equation. Panels (G–H) further show two different wave functions that are solutions of the Schrödinger equation but not standing waves.
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The Gaussian Integral is a beautiful integral for which the area between the e^(-x^2) and the x-axis from negative infinity to positive infinity perfectly equals the square root of pi. Image sources: 1, 2.
Remember to look up at the stars and not down at your feet. Try to make sense of what you see and wonder about what makes the universe exist. Be curious. And however difficult life may seem, there is always something you can do and succeed at. It matters that you don’t just give up.
Stephen Hawking, who turns 74 today. Happy birthday! (via astrowhat)
Looking at the stars from the inside of one of the Keck domes, at Mauna Kea.
Light behaves both as a particle and as a wave. Since the days of Einstein, scientists have been trying to directly observe both of these aspects of light at the same time. Now, scientists at EPFL have succeeded in capturing the first-ever snapshot of this dual behavior.
Read More - http://www.rdmag.com/videos/2015/03/first-ever-photograph-light-both-particle-and-wave
Math Bro sent me this and I didn’t watch it before an exam and that was a huge mistake. Always watch this before math exams. It’s important.
http://smbc-comics.com/comic/rocks