For this problem, we investigate the absorption spectra of a coupled double quantum well system. This problem elucidates not only the process of approaching these coupled systems, but also does a good job of how characterization of absorption spectra can be done from experimental data.
Category: quantum mechanics
Electron Spin
We work through an electron spin in an arbitrary direction, solving for the energy eigenvalues and eigenkets, as well as time evolving the system.
Free Particle
Here we investigate the wavefunction of a free particle, its expectation values both with and without time evolution, of an exponential function of the absolute value of x.
Particle in a Divided Box
Been a while since the last post since I’ve been working on typing up this long problem and have had some other work on my desk, but here is Sakurai 2.10. I make no guarantees of the validity of the result, but this should be an okay guide. This problem essentially gives us a particle in a state described by two wavefunctions, and then has us calculate energy eigenvalues of the system, time evolution, etc. This is a great problem for those still getting used to Dirac notation.
Potential Energy in the quantum SHO
Here I review the SHO from Griffiths, with a touch of Dirac notation. This problem is incredibly useful in highlighting SHO problems and their approach using the creation annihilation operators. I also mean for this to provide a bit of a stepping stone into Dirac notation, while leaving the wave function approach to Griffiths for readers to review to in order to see how this notation actually works.
Transformation Matrix
Here we look at the general idea of how to construct a transformation matrix, for use in quantum mechanics. A transformation matrix works to transform the state in some way, and there can be many different types of transformation operators, which makes them essential to understand. Here, I work through problem 1.26 from Sakurai, trying to provide ample thoughts and insights for the problem. This problem highlights a transformation matrix that transforms the Sz spin basis states to the Sx spin basis states.
Compatible and Degenerate Observables
Today we look at compatible and degenerate observables, utilizing Sakurai Problem 1.23 as an introduction. Compatible observables are very important in quantum mechanics, and understanding the initial concepts with the use of matrix form operators and eigenstates is very useful. Attached is a pdf with the foray into this problem and subject, and once again the validity is not guaranteed.
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