In 1985 Fridriech and Wintgen proposed a mechanism for bound states in the continuum based on full destructive interference of two resonances which can be easily applied to the two- and three-dimensional wave systems. Here we explicitly show that this mechanism can be realized in one-dimensional quantum potential well, owing to destructive interference of electron paths with different spin in tilted magnetic field. Due to one-by-one correspondence between the spin of the electron and the polarization state of light, we have found numerous bound states in the continuum in the one-dimensional photonic system and experimentally confirmed them. The experimental set-up consists of the one-dimensional photonic crystal conjugated with a liquid-crystalline anisotropic defect layer and covered by metal film.