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 documentation:language_reference:functions:rotate [2019/08/07 10:26]Simon Heinze documentation:language_reference:functions:rotate [2019/08/07 10:51] (current)Simon Heinze Major Update, including the mentioning of the rotation convention Both sides previous revision Previous revision 2019/08/07 10:51 Simon Heinze Major Update, including the mentioning of the rotation convention2019/08/07 10:26 Simon Heinze 2016/10/10 09:41 external edit2016/10/09 21:51 Maurits W. Haverkort created 2019/08/07 10:51 Simon Heinze Major Update, including the mentioning of the rotation convention2019/08/07 10:26 Simon Heinze 2016/10/10 09:41 external edit2016/10/09 21:51 Maurits W. Haverkort created Line 2: Line 2: ### ### - //​Rotate($\psi$,​ $R$)// ​or //​Rotate($O$,​ $R$)// rotates the basis of a wave-function ​or operator. + //​Rotate($M$,​ $R$)//, ​//​Rotate($\psi$,​ $R$)//, //Rotate($O$, $R$)// or //​Rotate($TB$, $R$)// rotates the basis of a quadratic matrix, ​a wave-function, an operator, or a tight-binding object (passive transformation). For a matrix it thus returns $R^\ast \cdot M \cdot R^T$, where $R^\ast$ denotes the complex conjugate and $R^T$ the transpose of the rotation matrix $R$. + + $R$ needs to be a matrix of dimension $N_1\times N_2$, where $N_2$ equals the number of rows of $M$, or $N_{Fermion}+N_{Boson}$ of $\psi$, $O$ or $TB$. The rotation matrix $R$ is not required to be quadratic, it is therefore possible to use rotations to change the number of dimensions of the Hilbert-space. + + $R^\ast \cdot R^T = 1$ is not checked by Quanty, to allow scaling rotations. + ### ### ===== Input ===== ===== Input ===== - * psi or Opp : Wavefunction ​or operator + * $M$, $\psi$, $O$ or $TB$ : a quadratic (complex ​or real valued) matrix, a wave-function,​ an operator, or a tight-binding object. - * rotmat ​: matrix of dimension NFermion+NBoson (table of tables) ​or real or complex numbers + * $R$ : a complex ​or real valued generalised rotation matrix. ===== Output ===== ===== Output ===== - * psi or Opp : Wavefunction or operator + * $M^\prime$, $\psi^\prime$, $O^\prime$ ​or $TB^\prime$ ​: the rotated quadratic matrix, wave-function, ​operator, or tight-binding object. ===== Example ===== ===== Example =====