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The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}

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Milewski J.

Banach Center Publications

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2007

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tom 78

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nr 1

265-273

EN

We consider equivariant solutions of Schrödinger equations on C∖{0} with harmonic oscillator potentials. We determine the spaces of equivariant quantum states in three cases: for an isotropic and anisotropic harmonic oscillator potential centered at 0, and for a potential not centered at 0.

2

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Holomorphons and the standard almost complex structure on \(S^6\)

100%

Milewski J.

Commentationes Mathematicae

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2006

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tom 46

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nr 2

EN

We consider Euler–Lagrange equations of families of nonnegative functionals defined on tensor fields of the type (1, 1), which are equal to zero only for complex structures tensor fields. As a solution of the equations we define the notion of holomorphon to distinguish a new class of tensor fields on Riemannian manifolds. Next, as our main result, we construct a holomorphon on the 6-dimensional sphere \(S^6\).

3

Holomorphons on spheres

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Milewski J.

Commentationes Mathematicae

|

2008

|

tom 48

|

nr 1

EN

We consider Euler–Lagrange equations of families of nonnegative functionals defined on tensor fields of the type \((1, 1)\), which are equal to zero only for complex structures tensor fields.

Ograniczanie wyników

2 Commentationes Mathematicae

1 Banach Center Publications

3 Milewski J.

1 2008

1 2007

1 2006

The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}

Holomorphons and the standard almost complex structure on \(S^6\)

Holomorphons on spheres