In this paper, we have implemented an unsupervised approach for finding out the significant genes from microarray gene expression datasets. The proposed method is based on implements a quantum clustering approach to represent gene-expression data as equations and uses the procedure to search for the most probable set of clusters given the available data. The main contribution of this approach lies in the ability to take into account the essential features or genes using clustering. Here, we present a novel clustering approach that extends ideas from scale-space clustering and support-vector clustering. This clustering method is used as a feature selection method. Our approach is fundamentally based on the representation of datapoints or features in the Hilbert space, which is then represented by the Schrödinger equation, of which the probability function is a solution. This Schrödinger equation contains a potential function that is extended from the initial probability function.The minima of the potential values are then treated as cluster centres. The cluster centres thus stand out as representative genes. These genes are evaluated using classifiers, and their performance is recorded over various indices of classification. From the experiments, it is found that the classification performance of the reduced set is much better than the entire dataset.The only free-scale parameter, sigma, is then altered to obtain the highest accuracy, and the corresponding biological significance of the genes is noted. © Springer Nature Singapore Pte Ltd 2020.