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The covariance matrix is one of the most useful compressed descriptions of a continuous-variable quantum state. It records the widths and corr...
The Wigner function is sometimes introduced merely as a way to draw a quantum state in phase space. That description is incomplete. When it is...
Quantum mutual information answers a concrete question: how much information is shared by two chosen subsystems? For continuous-variable syste...
The preceding chapters produced exact initial states and exact derivatives at the quench. A derivative is not a trajectory. To investigate osc...
Covariances describe widths and pairwise correlations. They do not describe an entire non-Gaussian wavefunction. A state can therefore have no...
The angular quench creates dynamics in a state that was stationary before $t=0$. The first experimentally accessible question is therefore loc...
A quantum quench is a rapid, controlled change of a Hamiltonian parameter. The state is continuous through an ideal sudden switch, but from th...
This chapter constructs exact non-Gaussian preparation states from the one-dimensional Schrödinger equation. The construction is algebraic: a ...
This chapter develops a two-dimensional charged oscillator from the basic minimal-coupling rule. No prior magnetic-oscillator calculation is a...
A charged harmonic oscillator in an external magnetic field appears to be a simple quantum-mechanical system, yet it provides a clean setting ...
Shape invariance is one of the central algebraic mechanisms behind exactly solvable quantum potentials in supersymmetric quantum mechanics. In...
Angular momentum in quantum mechanics is not merely the quantization of $\mathbf{L}=\mathbf{r}\times\mathbf{p}$. That formula describes one sp...
We study a two-degree-of-freedom model with a velocity-coupling term and an inverse-square interaction. The classical dynamics becomes transpa...
Advanced concepts in Lagrangian mechanics, including generalized coordinates, nonstandard Lagrangians, and coupled systems.
Exact Solution on Shifted Contour Starting from the radial Schrödinger equation on the complex-shifted contour $r=x-i\varepsilon,; x\in(-\inft...
A defining insight of modern theoretical physics is that the fundamental laws of nature are governed not merely by differential equations, but...
Why Study Lie Superalgebras in Supersymmetry
The harmonic oscillator provides the simplest setting where operator factorization leads naturally to supersymmetric structure. The Hamiltonia...
The progression of theoretical physics has shown time and time again that advancements are generally made when the underlying mathematical str...
As modern physics has developed, it has shown that the expansion of the concept of symmetry has led to new insights into the nature of the fun...
Recent developments in physics have highlighted the importance of continuous symmetry as a means to establish a connection between geometry an...
Symmetry is fundamental to physics today, because it provides a common language bridging abstract mathematics with observable phenomena. In cl...
There are several distinct definitions and constructions of coherent states in the literature, each with its own mathematical formulation, phy...
The non-Gaussianity (nonG) of a continuous-variable (CV) quantum state $ \rho $ is defined as the quantum relative entropy distance between $ ...
A celebrated phase-space description of nonclassicality in single-mode quantum oscillators is based on the presence of negative regions of the...
The basic idea of contour integration is to extend the concept of integration from the real line to the complex plane. Instead of integrating ...
By M. Lieber Received 18 June 1974
On the Theory of the Hydrogen Atom by V. Fock, Leningrad (Received August 5, 1935)
Theory of the Hydrogen Atom
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