\( \def\ket#1{{ \left| #1 \right> }} \) \( \def\bracket#1{{ \left( #1 \right) }} \) Usually in a quantum mechanics course, Schrodinger picture is introduced along with the Schrodinger equation \begin{equation} \hat{H} \ket{\psi(t)} = i \hbar \frac{\partial}{\partial t}\ket{\psi (t)}, \end{equation} where the quantum state $\ket{\psi(t)}$ evolves in time but quantum operators, like Hamiltonian $\..
Say, I was studying a physics topic, for example Bloch's theorem, from textbooks. I asked myself these questions: what does the theorem state? What are conditions to apply the theorem? Can I explain the theorem by usual physical sense? , etc. Then, I worked on the mathematics related to the theorem. I wrote down the mathematical form of Bloch theorem, used translational symmetry of Hamiltonian t..
The avatar of my blog is graph of Hofstadter's butterfly which results from a 2D lattice subjected to an external magnetic field. To generate the graph, I consider a squared lattice lying on xy-plane to which a z-direction magnetic field is applied. I use tight-binding model to construct the system's Hamiltonian and numerically solve the energy spectrum's dependence on magnetic flux through a la..
Physics Corner 2022. 5. 2. 01:07
\( \def\ket#1{{ \left| #1 \right> }} \) \( \def\bracket#1{{ \left( #1 \right) }} \) Usually in a quantum mechanics course, Schrodinger picture is introduced along with the Schrodinger equation \begin{equation} \hat{H} \ket{\psi(t)} = i \hbar \frac{\partial}{\partial t}\ket{\psi (t)}, \end{equation} where the quantum state $\ket{\psi(t)}$ evolves in time but quantum operators, like Hamiltonian $\..
Physics Corner 2022. 4. 30. 23:28
Say, I was studying a physics topic, for example Bloch's theorem, from textbooks. I asked myself these questions: what does the theorem state? What are conditions to apply the theorem? Can I explain the theorem by usual physical sense? , etc. Then, I worked on the mathematics related to the theorem. I wrote down the mathematical form of Bloch theorem, used translational symmetry of Hamiltonian t..
Physics Corner 2022. 4. 19. 13:39
The avatar of my blog is graph of Hofstadter's butterfly which results from a 2D lattice subjected to an external magnetic field. To generate the graph, I consider a squared lattice lying on xy-plane to which a z-direction magnetic field is applied. I use tight-binding model to construct the system's Hamiltonian and numerically solve the energy spectrum's dependence on magnetic flux through a la..