Traditional search engines usually provide identical search results for all users, overlooking individual preferences. To counter this limitation, personalized search has been developed to re-rank results based on user preferences derived from query logs. Deep learning-based personalized search methods have shown promise, but they rely heavily on abundant training data, making them susceptible to data sparsity challenges. This paper proposes a Cognitive Personalized Search (CoPS) model, which integrates Large Language Models (LLMs) with a cognitive memory mechanism inspired by human cognition. CoPS employs LLMs to enhance user modeling and user search experience. The cognitive memory mechanism comprises sensory memory for quick sensory responses, working memory for sophisticated cognitive responses, and long-term memory for storing historical interactions. CoPS handles new queries using a three-step approach: identifying re-finding behaviors, constructing user profiles with relevant historical information, and ranking documents based on personalized query intent. Experiments show that CoPS outperforms baseline models in zero-shot scenarios.