We apply methods of wave mechanics to financial modelling. We proceed by assigning a financial interpretation to wave numbers. This paper makes a plea for the use of the concept of 'tunnelling' (in the mathematical formalism of quantum mechanics) in the modelling of financial arbitrage. Financial arbitrage is a delicate concept to model in social science (i.e. in this case economics and finance) as its presence affects the precision of benchmark financial asset prices. In this paper, we attempt to show how 'tunnelling' can be used to positive effect in the modelling of arbitrage in a financial asset pricing context.