%0 Journal Article %1 springerlink:10.1007/s10910-012-0012-z %A Simpao, Valentino %D 2012 %I Springer Netherlands %J Journal of Mathematical Chemistry %K equation laplace mechanics physics quantum schrodinger solution transform %N 7 %P 1931-1972 %R 10.1007/s10910-012-0012-z %T HOA (Heaviside Operational Ansatz) revisited: recent remarks on novel exact solution methodologies in wavefunction analysis %U http://dx.doi.org/10.1007/s10910-012-0012-z %V 50 %X A viable methodology for the exact analytical solution of the multiparticle Schrodinger and Dirac equations has long been considered a holy grail of theoretical chemistry. Since a benchmark work by Torres-Vega and Frederick in the 1990s, the QPSR (Quantum Phase Space Representation) has been explored as an alternate method for solving various physical systems. Recently, the present author has developed an exact analytical symbolic solution scheme for broad classes of differential equations utilizing the HOA (Heaviside Operational Ansatz). An application of the scheme to chemical systems was initially presented in Journal of Mathematical Chemistry (Toward chemical applications of Heaviside Operational Ansatz: exact solution of radial Schrodinger equation for nonrelativistic N-particle system with pairwise 1/ r ( I ) radial potential in quantum phase space. Journal of Mathematical Chemistry, 2009 ; 45(1):129–140). It is believed that the coupling of HOA with QPSR represents not only a fundamental breakthrough in theoretical physical chemistry, but it is promising as a basis for exact solution algorithms that would have tremendous impact on the capabilities of computational chemistry/physics. The novel methods allow the exact determination of the momentum and configuration space wavefunction from the QPSR wavefunction by way of a Fourier transform. In this note some remarks, examples and further directions, concerning HOA as a tool to solve and provide analytical insight into solutions of dynamical systems occurring in, but not limited to Mathematical Chemistry, are also posited.

@article{springerlink:10.1007/s10910-012-0012-z, abstract = {A viable methodology for the exact analytical solution of the multiparticle Schrodinger and Dirac equations has long been considered a holy grail of theoretical chemistry. Since a benchmark work by Torres-Vega and Frederick in the 1990s, the QPSR (Quantum Phase Space Representation) has been explored as an alternate method for solving various physical systems. Recently, the present author has developed an exact analytical symbolic solution scheme for broad classes of differential equations utilizing the HOA (Heaviside Operational Ansatz). An application of the scheme to chemical systems was initially presented in Journal of Mathematical Chemistry (Toward chemical applications of Heaviside Operational Ansatz: exact solution of radial Schrodinger equation for nonrelativistic N-particle system with pairwise 1/ r ( I ) radial potential in quantum phase space. Journal of Mathematical Chemistry, 2009 ; 45(1):129–140). It is believed that the coupling of HOA with QPSR represents not only a fundamental breakthrough in theoretical physical chemistry, but it is promising as a basis for exact solution algorithms that would have tremendous impact on the capabilities of computational chemistry/physics. The novel methods allow the exact determination of the momentum [and configuration] space wavefunction from the QPSR wavefunction by way of a Fourier transform. In this note some remarks, examples and further directions, concerning HOA as a tool to solve and provide analytical insight into solutions of dynamical systems occurring in, but not limited to Mathematical Chemistry, are also posited.}, added-at = {2012-10-07T18:19:47.000+0200}, affiliation = {Mathematical Consultant Services, 108 Hopkinsville St., Greenville, KY 42345, USA}, author = {Simpao, Valentino}, biburl = {https://www.bibsonomy.org/bibtex/23689c98e0f3b0c3da6549cafb1324531/drmatusek}, description = {Journal of Mathematical Chemistry, Volume 50, Number 7 - SpringerLink}, doi = {10.1007/s10910-012-0012-z}, interhash = {3c51093dba0232d478ed07f1711b8ca1}, intrahash = {3689c98e0f3b0c3da6549cafb1324531}, issn = {0259-9791}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {equation laplace mechanics physics quantum schrodinger solution transform}, month = aug, number = 7, pages = {1931-1972}, publisher = {Springer Netherlands}, timestamp = {2012-10-18T03:59:53.000+0200}, title = {HOA (Heaviside Operational Ansatz) revisited: recent remarks on novel exact solution methodologies in wavefunction analysis}, url = {http://dx.doi.org/10.1007/s10910-012-0012-z}, volume = 50, year = 2012 }