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Consider a Schrödinger operator $H:=-\Delta+V$ on $\mathbb R$, where $V$ is such that $H$ has a purely discrete spectrum $-\infty<\lambda_1\leq\lambda_2\leq\cdots$ converging to $+\infty$. Do there ...

Conside the One dimentional Schrodinger Operator $$ -\frac{d^2}{dx^2} + ( V(x) + E ) $$ Where the Potential Function $V$ is of the form $V(x) = ax^2 + b^2x^4$ , $a,b \in \mathbb{R} $. What is known ...

I'm new to this site, but I felt the need to post when I recently came in to an ordinary differential equation/boundary value problem with this form: $(1)- \frac{d^2 y}{d x^2} + \frac{m(m+1)} {x^2(...

Differential equations of the form $$\frac{d}{dt}\vec{x} = - \nabla E(\vec{x})$$ can be analyzed using phase portrait method. In particular, if the function $E$ (we call it energy) has local minimums, ...

I am interested in a characterization of the creation and annihilation operators that is in some sense invariant under $O(n)$ rotations of $\mathbb{R}^n$: Background The Harmonic Oscillator on $\...