2. MAIN RESULT 4 Problem 1 can be reduced to an inverse source problem. For this aim, let v ( p ) and v ( q ) be two solutions of (1.1)–(1.3) with the coefficients p and q respectively. Then the difference u = v ( p ) − v ( q ) satisfies Au = i∂$_{t}$u ( x, y, t ) + Δ$_{y}$ u ( x, y, t ) − Δ$_{x}$ u ( x, y, t ) − p ( x, y ) u ( x, y, t ) = f ( x, y ) R ( x, y, t ) , ( x, y, t ) ∈ Q, (2.1) u ( x, y, 0) = 0 , ( x, y ) ∈ D × G, (2.2) u ( x, y, t ) = 0 , ( x, y, t ) ∈ Σ (2.3) u = 0 on ∂D × {| y | < 2 L } × ( − T, T ) , ∥ ∂ k t u ∥ H $^{2}$( D ×{| y | < 2 L }× ( − T,T )) ≤ M, k = 1 , 2 and R ( x, y, 0) ∈ R or iR ( x, y, 0) ∈ R a. e. in ( D × {| y | < 2 L } ) , R ∈ H $^{2}$( − T, T ; L $^{∞}$( D × {| y | < 2 L } )) , ∥ ∂ k t R ∥ L $^{2}$( − T,T ; L $^{∞}$( D ×{| y | < 2 L } )) ≤ M, k = 1 , 2 . We assume that with f ( x, y ) = p ( x, y ) − q ( x, y ) and R = v ( q )( x, y, t ) . We consider the following inverse source problem: Problem 2 Let p, R be given suitably. Then determine f ( x, y ) , ( x, y ) ∈ D × G by the extra data ∂$_{ν}$u | $_{Σ}$. Here we do not assume the uniqueness of v ( p ) and v ( q ) but their existence. We have the following result for Problem 2. Theorem 1 Let p ∈ L $^{∞}$( D × {| y | < 2 L } ) and u satisfy (2.1)–(2.3) in D ×{| y | < 2 L } × ( − T, T ) .