Improvement of the envelope theory with the dominantly orbital state method

The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$ dimensions. The quality of the approximate eigenvalues can be improved by adding a free parameter in the characteristic global quantum number of the solutions. A method is proposed to determine the value of this parameter by comparing the eigenvalues computed with the envelope theory to the corresponding ones computed with a $N$-body generalization of the dominantly orbital state method. The accuracy of the procedure is tested with several systems.

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