Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

Crocodile farms and management of saltwater crocodiles in Northern Territory: Results of a survey of NT crocodile farmers plus analysis of secondary information

After outlining some relevant background information about the NT crocodile farming industry and explaining the purpose of our survey of NT crocodile farmers conducted in the first half of 2005, this paper reports the results of the survey. The information received from the survey is supplemented by secondary data and by information from secondary sources. This report covers the location of respondents; the size of crocodile farms; farmers’ stated knowledge of and attitudes towards the NT Crocodile Management Plan; the involvement of farms in the harvesting of crocodile eggs and the costs involved; views of crocodile farmers about whether the NT Crocodile Management Plan encourages landholders to conserve crocodiles and their perceptions of the benefits to landholders; predicted production trends and trends in the number of farms operating in NT; economic characteristics of crocodile farms producing in NT including the economic advantages and disadvantages of crocodile farming in NT. Concluding comments provide, amongst other things, an overview of the structure of the crocodile farming industry in the NT gleaned from a consideration of data available from the NT Government’s Department of Business, Industry and Resource Development.

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.