This study aims to model and forecast the nonlinear distribution of stock returns using quantum-finance approaches. It is applied and ex post facto in design, using quarterly data from the first quarter of 2011 to the first quarter of 2025. Initially, 137 potential determinants of stock returns were screened using model-averaging approaches, including Bayesian Model Averaging (BMA), Weighted Average Least Squares (WALS), and Dynamic Model Averaging and Selection. The results indicate that WALS provides a more stable structure and superior performance, identifying 12 influential variables, among which earnings per share is the most important positive determinant, while the debt ratio is the strongest adverse factor. Subsequently, the return distribution was modeled and forecast using effective potential and the nonlinear Schrödinger equation within discrete and continuous quantum-finance models. The findings show that discrete models perform particularly well at short horizons, whereas continuous models exhibit greater stability and more accurately reproduce the overall return distribution at longer horizons.