Year 2018

• Simple Fractal Calculus from Fractal Arithmetic

  Publication

  • D. Aerts
  • M. Czachor
  • M. Kuna

  - REPORTS ON MATHEMATICAL PHYSICS - Year 2018

  Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued...

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Year 2010

• General solution of quantum mechanical equations of motion with time-dependent Hamiltonians: A Lie algebraic approach

  Publication

  • M. Kuna
  • J. Naudts

  - REPORTS ON MATHEMATICAL PHYSICS - Year 2010

  The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). In these cases we give explicit formulae for obtaining general solutions from special ones. We show that the constructions...

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