The MCTDH Package. MCTDH stands for Multi Configuration Time Dependent Hartree. MCTDH is a general algorithm to solve the time-dependent Schrödinger equation for multidimensional dynamical systems consisting of distinguishable particles. MCTDH can thus determine the quantal motion of the nuclei of a molecular system evolving on one or several coupled electronic potential energy surfaces. MCTDH by its very nature is an approximate method. However, it can be made as accurate as any competing method, but its numerical efficiency deteriorates with growing accuracy.

References in zbMATH (referenced in 20 articles )

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  1. Musharbash, Eleonora; Nobile, Fabio: Dual dynamically orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions (2018)
  2. Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em: A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems (2017)
  3. Burkhard Schmidt, Carsten Hartmann: WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction (2017) arXiv
  4. Burkhard Schmidt, Ulf Lorenz: WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations (2017) arXiv
  5. Bachmayr, Markus; Schneider, Reinhold; Uschmajew, André: Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations (2016)
  6. Lubich, Christian; Oseledets, Ivan V.; Vandereycken, Bart: Time integration of tensor trains (2015)
  7. Rauhut, Holger; Schneider, Reinhold; Stojanac, Željka: Tensor completion in hierarchical tensor representations (2015)
  8. Grasedyck, Lars; Kressner, Daniel; Tobler, Christine: A literature survey of low-rank tensor approximation techniques (2013)
  9. Holtz, Sebastian; Rohwedder, Thorsten; Schneider, Reinhold: On manifolds of tensors of fixed TT-rank (2012)
  10. Khoromskij, Boris N.: $O(d \log N)$-quantics approximation of $N$-$d$ tensors in high-dimensional numerical modeling (2011)
  11. Bardos, Claude; Catto, Isabelle; Mauser, Norbert; Trabelsi, Saber: Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations (2010)
  12. Bardos, Claude; Mauser, Norbert J.: One particle equations for many particle quantum systems: the MCTHDF method (2010)
  13. Conte, Dajana; Lubich, Christian: An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics (2010)
  14. Koch, Othmar; Ede, Christopher; Jordan, Gerald; Scrinzi, Armin: Hierarchical matrices in computations of electron dynamics (2010)
  15. Xu, Dong; Stare, Jernej; Cooksy, Andrew L.: Solving the vibrational Schrödinger equation on an arbitrary multidimensional potential energy surface by the finite element method (2009)
  16. Nonnenmacher, Achim; Lubich, Christian: Dynamical low-rank approximation: Applications and numerical experiments (2008)
  17. Koch, Othmar; Lubich, Christian: Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics (2007)
  18. Trabelsi, Saber: Solutions of the multiconfiguration time-dependent Hartree-Fock equations with Coulomb interactions (2007)
  19. Koch, Othmar; Kreuzer, Wolfgang; Scrinzi, Armin: Approximation of the time-dependent electronic Schrödinger equation by MCTDHF (2006)
  20. Lubich, Christian: A variational splitting integrator for quantum molecular dynamics. (2004)

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