The effect of proximity to an infinite potential wall boundary on the elgenvalues of single particle free electron states in a magnetic field is calculated. A general method for calculating the number of states below a specified energy is described and the diamagnetic susceptibility is calculated for three approximations, It is found that the Landau approximation gives surprisingly good results considering its simplicity. A classification of much of the important work in this subject is presented in the introduction, and a possible discrepancy in the usual applications of the WKB approximation is discussed in an appendix.