We present an improved version of Berry’s ansatz able to incorporate exactly the existence of boundaries and the correct normalization of the eigenfunction into an ensemble of random waves. We then reformulate the Random Wave conjecture showing that in its new version it is a statement about the universal nature of eigenfunction fluctuations in systems with chaotic classical dynamics. The emerg...

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular exam...

This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing is then immediate by the linearity property of the pricing operator and the eigenvector property...

An analytic method originated by Y. H. Chin was extended to calculate the electromagnetic fields and the longitudinal impedance due to coherent wiggler radiation (CWR) in a rectangular chamber. The method used dyadic Green functions based on eigenfunction expansion method in electromagnetic theory and was rigorous for the case of straight chamber. We re-derived the theory and did find the full ...

A novel approach is suggested to compute the response of discretized stochastic elliptic partial differential equations by utilising the stochastic finite element analysis method. The mathematical form of the approach is established by projecting random scalars onto a random basis. By implementing an eigendecomposition of a system’s stiffness matrix, the random scalars and random basis are comp...

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function...