Brain inspired spiking neural networks (SNNs) have been successfully applied to many pattern recognition domains. The SNNs based deep structure have achieved considerable results in perceptual tasks, such as image classification, target detection. However, the application of deep SNNs in reinforcement learning (RL) tasks is still a problem to be explored. Although there have been previous studies on the combination of SNNs and RL, most of them focus on robotic control problems with shallow networks or using ANN-SNN conversion method to implement spiking deep Q Network (SDQN). In this work, we mathematically analyzed the problem of the disappearance of spiking signal features in SDQN and proposed a potential based layer normalization(pbLN) method to directly train spiking deep Q networks. Experiment shows that compared with state-of-art ANN-SNN conversion method and other SDQN works, the proposed pbLN spiking deep Q networks (PL-SDQN) achieved better performance on Atari game tasks.