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On the First-Order Raising Operators for the Hamiltonians in Two Variables

Yoshihiko Miyachi, Yasutaro Takao

Progress of Theoretical PhysicsMay 1, 19760 citations

Universal Raising and Lowering Operators for a Discrete Energy Spectrum

Gabino Torres-Vega

Foundations of PhysicsMar 8, 20161 citation

Exact operator solutions to Euler hamiltonians

Carl M. Bender, Gerald V. Dunne

Physics Letters BJan 1, 198815 citations

Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model

Akira Takamura

We algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. We introduce the following characteristic operators and systematically produce all the eigenstates starting from the ground state by multiplying the operators. The braid-exclusion operators exchange eigenvalues of pseudomomenta; they follow the algebra of a braid group and also include effects of the exclusion statistics. The raising and lowering operators increase and decrease eigenvalues of pseudomomenta. The Sutherland model is a solvable quantum many-body system with inversesquare interaction on a circumference [1]. The ground-state wave function is of the Jastrow type and excited states are represented as polynomials multiplied by the ground state. Among the polynomials symmetric ones are the Jack polynomials [2, 3, 4], while the others are called nonsymmetric Jack polynomials. These states can be taken as eigenstates of the pseudomomenta or DunkelWe algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. We introduce the following characteristic operators and systematically produce all the eigenstates starting from the ground state by multiplying the operators. The braid-exclusion operators exchange eigenvalues of pseudomomenta; they follow the algebra of a braid group and also include effects of the exclusion statistics. The raising and lowering operators increase and decrease eigenvalues of pseudomomenta. The Sutherland model is a solvable quantum many-body system with inversesquare interaction on a circumference [1]. The ground-state wave function is of the Jastrow type and excited states are represented as polynomials multiplied by the ground state. Among the polynomials symmetric ones are the Jack polynomials [2, 3, 4], while the others are called nonsymmetric Jack polynomials. These states can be taken as eigenstates of the pseudomomenta or Dunkel

Jan 1, 19983 citations

Simplified quantum oscillator solution

Thomas F. Jordan

To find the eigenvalues and eigenvectors of the quantum oscillator Hamiltonian, it is enough to construct eigenvectors with the raising operator and see that these eigenvectors are complete. The subspace they span must be the entire space of square-integrable functions because it is invariant for the raising and lowering operators and therefore invariant for the position and momentum operators. This shows that the Hamiltonian has no continuous spectrum.

American Journal of PhysicsOct 1, 20011 citation

On the determination of quantum Hamiltonians

Chai Yan

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BMar 1, 19840 citations

Raising and lowering operators for nonsymmetric Hamiltonians

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Raising and lowering operators for nonsymmetric Hamiltonians

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