A new formalism has been elaborated for calculations of hydrogen line profiles emitted by dense plasmas. Calculated line shapes are broadened, shifted and asymmetrical. The formalism is very general and yields full line shapes, shifts and widths at relatively small number of assumptions. For this purpose a new basis of the appropriate subspace of the Hilbert space has been built. This basis gives an accurate description of the quadratic Stark effect and the interaction of the emitter with field gradients. A computer simulation has been used to determine the emitter perturbations by electrons and ions. Final results have been compared with experimental and theoretical findings of other authors.