Archive of posts with tag “quantum mechanics”
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From Picard iteration to Feynman path integral
The Schrödinger equation is an ODE, so we can approach its solution through Picard iteration. This approach leads to a sum over walks on the graph formed by an orthonormal basis as vertices and the Hamiltonian matrix elements as edge weights. This sum is exactly the Feynman path integral if we choose the position basis and take the continuum limit. -
The role of particle indistinguishability in statistical mechanics
Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics. -
The smallest wave packet in the lowest Landau level
The smallest wave packet in the lowest Landau level exists, and is a Gaussian wave packet. This turns out to be related to the coherent state of the harmonic oscillator. -
You can replace with in the Schrödinger equation?
When someone asks you why it is here instead of or the other way around, you can say that this is just a convention. My professor of quantum mechanics once asked the class similar a question, and I replied with this letter. -
Introducing bra–ket notation to math learners
Bra–ket notation is a good-looking notation! I am sad that it is not generally taught in math courses. Let me introduce it to you. -
Even solutions to bound states in an odd number of potential wells
We try solving the even function solutions to the time-independent Schrödinger equation for the potential such that (bound states).
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