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We derive the classical analog of the extended phase space quantum mechanicsof the particle with odd degrees of freedom which gives rise to(N=2)-realization of supersymmetry (SUSY) algebra. By means of an iterativeprocedure, we find the approximate groundstate solutions to the extendedSchr\"{o}dinger-like equation and use these solutions further to calculate theparameters which measure the breaking of extended SUSY such as the groundstateenergy. Consequently, we calculate a more practical measure for the SUSYbreaking which is the expectation value of an auxiliary field. We analyzenon-perturbative mechanism for extended phase space SUSY breaking in theinstanton picture and show that this has resulted from tunneling between theclassical vacua of the theory. Particular attention is given to the algebraicproperties of shape invariance and spectrum generating algebra.

Classical analog of extended phase space SUSY and its breaking