. "RIV/61389005:_____/03:49033079" . . . . "A new type of exact solvability is reported. The Schrodinger equation is considered in a very large spatial dimension D much greater than 1 and its central polynomial potential is allowed to depend on 'many' (= 2q) coupling constants. In a search for its bound states possessing an exact and elementary wavefunction (proportional to a harmonic-oscillator-like polynomial of a freely varying, i.e., not just small, degree N), the 'solvability conditions' are known to form a complicated nonlinear set which requires a purely numerical treatment at a generic choice of D, q and N. Assuming that D is large we discovered and demonstrate that this problem may be completely factorized and acquires an amazingly simple exact solution at all N and up to q = 5 at least."@en . . "6531;6549" . "36" . "23" . "A new type of exact solvability is reported. The Schrodinger equation is considered in a very large spatial dimension D much greater than 1 and its central polynomial potential is allowed to depend on 'many' (= 2q) coupling constants. In a search for its bound states possessing an exact and elementary wavefunction (proportional to a harmonic-oscillator-like polynomial of a freely varying, i.e., not just small, degree N), the 'solvability conditions' are known to form a complicated nonlinear set which requires a purely numerical treatment at a generic choice of D, q and N. Assuming that D is large we discovered and demonstrate that this problem may be completely factorized and acquires an amazingly simple exact solution at all N and up to q = 5 at least." . . "[7E0B582B0E29]" . . . "exact solution; large-N limit; anharmonic-oscillators"@en . "Gerdt, V. P." . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "1"^^ . "19"^^ . "3"^^ . "New exact solutions for polynomial oscillators in large dimensions."@en . "0"^^ . . "0"^^ . . "New exact solutions for polynomial oscillators in large dimensions." . . "Znojil, Miloslav" . "P(KSK1010104)" . "617842" . . "New exact solutions for polynomial oscillators in large dimensions." . "Yanovich, D." . . . "RIV/61389005:_____/03:49033079!RIV/2004/AV0/A49004/N" . . "New exact solutions for polynomial oscillators in large dimensions."@en . "JOURNAL OF PHYSICS. A-MATHEMATICAL AND GENERAL" . "0305-4470" .