vorsichtiger Ansatz - translation to English
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vorsichtiger Ansatz - translation to English

AN ANSATZ METHOD FOR FINDING THE EXACT SOLUTIONS OF CERTAIN ONE-DIMENSIONAL QUANTUM MANY-BODY MODELS
Bethe approximation; Bethe's ansatz; Bethe Ansatz

vorsichtiger Ansatz      
careful approach, cautious advance, careful try
careful approach      
vorsichtige Einstellung, vorsichtiger Ansatz

Wikipedia

Bethe ansatz

In physics, the Bethe ansatz is an ansatz method for finding the exact wavefunctions of certain one-dimensional quantum many-body models. It was invented by Hans Bethe in 1931 to find the exact eigenvalues and eigenvectors of the one-dimensional antiferromagnetic Heisenberg model Hamiltonian. Since then the method has been extended to other models in one dimension: the (anisotropic) Heisenberg chain (XXZ model), the Lieb-Liniger interacting Bose gas, the Hubbard model, the Kondo model, the Anderson impurity model, the Richardson model etc.