  This paper investigates the notion of Krylov complexity, a measure of
operator growth, within the framework of 1-matrix quantum mechanics (1-MQM).
Krylov complexity quantifies how an operator evolves over time by expanding it
in a series of nested commutators with the Hamiltonian. We analyze the Lanczos
coefficients derived from the correlation function, revealing their linear
growth even in this integrable system. This growth suggests a link to chaotic
behavior, typically unexpected in integrable systems. Our findings in both
ground and thermal states of 1-MQM provide new insights into the nature of
complexity in quantum mechanical models and lay the groundwork for further
studies in more complex holographic theories.
