The paper presents a third-order nonlinear differential equation (Eq. 6) whose imaginary part, integrated over x, yields the correlation kernel K(E,E') for Schrodinger-type random matrix models, generalizing the Gel'fand-Dikii equation.
The Simplest Model —The special “Bessel” models have potential u(x)=ℏ2(Γ2− 1 4)/x2, where Γ is an inte- ger or half integer [11]
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A differential equation for a class of correlation kernels
The paper presents a third-order nonlinear differential equation (Eq. 6) whose imaginary part, integrated over x, yields the correlation kernel K(E,E') for Schrodinger-type random matrix models, generalizing the Gel'fand-Dikii equation.