Abstract
The bases used in quantum mechanics, in general, are orthonormal. The relations in orthonormal basis vectors are simpler than those in nonorthogonal basis vectors. Also, the operators that represent different physical quantities are Hermitian and the eigenvectors of these operators belonging to different eigenvalues are orthonormal to each other. But, in many cases, such as sets of screened hydrogenic wavefunctions, nonorthogonal sets of basis vectors occur. It is, therefore, necessary to consider the representation of vectors and operators in nonorthogonal bases. Making use of the set of vectors reciprocal to the given set of nonorthogonal base vectors, the expression for the norms of vectors and for the matrix elements has been found. Also, adjoint and Hermitian matrices in nonorthogonal bases have been worked out using a set of reciprocal basis vectors.
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