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We derive a normally ordered disentanglement or splitting formula for exponentials of the infinite-dimensional Schrödinger Lie algebra generators. As an application we compute the vacuum characteristic function of a quantum random variable defined as a self-adjoint finite sum of Fock space operators, satisfying the multi-dimensional Schrödinger Lie algebra commutation relations.

Normally Ordered Disentanglement of Multi-Dimensional Schrödinger Algebra Exponentials