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| material:qmodel [2025/08/01 09:27] – [Methods] markus | material:qmodel [2025/08/02 14:25] (current) – [Methods] markus |
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| ===== Basis class ===== | ===== Basis class ===== |
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| | A basis is subscriptable, meaning that ''b[i]'' returns the //i//th element of the basis as a ''Vector'' (where ''i'' starts with 0). |
| ==== Properties ==== | ==== Properties ==== |
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| ''tensor_basis'' is an optional argument to fix a 2-particle basis for the returned vector. If it is not given, a new basis is constructed as a tensor product of the vectors' bases. It might be necessary to specify ''tensor_basis'' in many cases, since the new vector should be defined on a particular basis object. More importantly, the symmetry of the provided basis is also respected. If ''tensor_basis'' is symmetric, the tensor product is a symmetrized tensor product, $v\otimes w+w\otimes v$, if it is antisymmetric, the tensor product is a wedge product, $v\wedge w=v\otimes w-w\otimes v$. | ''tensor_basis'' is an optional argument to fix a 2-particle basis for the returned vector. If it is not given, a new basis is constructed as a tensor product of the vectors' bases. It might be necessary to specify ''tensor_basis'' in many cases, since the new vector should be defined on a particular basis object. More importantly, the symmetry of the provided basis is also respected. If ''tensor_basis'' is symmetric, the tensor product is a symmetrized tensor product, $v\otimes w+w\otimes v$, if it is antisymmetric, the tensor product is a wedge product, $v\wedge w=v\otimes w-w\otimes v$. |
| | </WRAP> |
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| | ''**Vector.proj() -> Operator**'' |
| | <WRAP indent> |
| | Returns an operator that is the projector on the given vector. |
| | The vector is always normalized in the procedure. |
| </WRAP> | </WRAP> |
| ===== Operator class ===== | ===== Operator class ===== |
| ''**Operator.norm() -> float**'' | ''**Operator.norm() -> float**'' |
| <WRAP indent> | <WRAP indent> |
| Return the 2-norm (largest singular value) of an operator. | Return the 2-norm (largest singular value) of the operator. |
| | </WRAP> |
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| | ''**Operator.trace() -> complex**'' |
| | <WRAP indent> |
| | Return the trace (sum over all diagonal values) of the operator. |
| </WRAP> | </WRAP> |
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