Home page for D Richards
Applied Mathematics Department
Mathematics & Computing Faculty
The Open University
Milton Keynes MK7 6AA
Tel: +44 1908 653507 (dd) (653580 sec)
Fax: +44 1908 652140
Email Address: D.Richards@open.ac.uk
Books
- Introduction to Dynamics I C Percival and D Richards (Cambridge
University Press, 1982)
An errata list is given
here
- Advanced Mathematical Methods with Maple (Cambridge
University Press, published, November 2001).
There are over
1000 exercises in this book many solutions of which may be obtained by
going here .
A list of errata is
here .
Courses
- M820 The Calculus of Variations and Advanced Calculus
This course comprises 14 chapters, which may be viewed from
here ; the solutions to all the exercises
are here .
These notes were last corrected in January 2011,
taking account of all errors known at this time.
M821 Nonlinear Differential Equations
There is no errata list at present.
Research interests
- Nonlinear classical systems and their corresponding
quantal analogue.
Topics of current interest
Excerpt from current research degree prospectus ...
-
Studying the manner in which the chaotic phenomena observed in the motion
of most classical nonlinear systems are manifest in the equivalent quantal
systems. The research concentrates on systems accessible to experiments,
particularly strong time-dependent electric fields on excited atoms, and
there is a fruitful collaboration with Professor P M Koch's experimental
group at Stony Brook. The main aims of the work are to understand the
general features of the classical and quantal motion of systems perturbed
by strong time-dependent forces; and to understand the circumstances in
which classical and quantum observables behave similarly and when they differ.
Recent publications and preprints
- Core-induced chaos in intra-shell transitions. With D Fregenal, M Forre
and E Hrsdal. Submitted to Phys Rev A.
Reprint
- The effect of parallel static and microwave electric fields on
excited hydrogen atoms. Published in New J Phys.
7 (2005) 138. Reprint
- Intensity-dependent dispersion under conditions of electromagnetically
induced transparency in coherently prepared multistate atoms.
Phys Rev A 67 023818-1:5 (2003)
- A Scaling law for the energy levels of a non-linear schrodinger equation.
J.Phys. B34, 1805-1813 (2001) Preprint
- Appearing and Disappearing Strong-Field Resonances in H atoms. Phys. Rev
A61, 060101-1 (2000)
- Stochastic wave functions diagrams for electromagnetically induced
transparency, inversionless gain and shelving. J Mod Opt 54,
315-333 (1998).
- Stochastic Schrodinger equations for optical fields based on atom
detection, Phys Rev A58, 2690-2698 (1998).
- Stark-state resonances induced by low-frequency elliptically polarised
fields. J. Phys B30 4019-4047 (1997)
Preprint
- Resonant, elliptical-polarisation control of microwave ionisation
of hydrogen atoms. Phys. Rev Lett 78, 3840-3843 (1997).
- The Periodically Driven Excited Hydrogen Atom .
A review article in Classical, Semiclassical and Quantum Dynamics
in Atoms 1997, (Springer, Lecture notes in Physics)
Preprint
- Polarisation independence of microwave ionisation thresholds of
excited hydrogen atoms near the principle resonance. Phys Rev Lett 76,
892-895 (1996).
- The effects of classical resonance islands in time-dependent
quantum mechanics. J. Phys. B29, 5237-5271, (1996).
Preprint
- The dynamics of high harmonic generation. J Phys. B29,
2935-2949 (1996). Preprint
- One-dimensional excited hydrogen atoms in short-pulsed high frequency
fields. J. Phys B28 L413-L421 (1995).
- Robust scarred states. J Phys B27 2169-2189 (1994).
Applied Maths
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