Abstract
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 $D$-dimension. The accuracy of this method is tested by computing the ground state of $N$ identical bosons for various systems. A method is proposed to improve the quality of the approximations by modifying the characteristic global quantum number of the method.
Highlights
The envelope theory (ET), known as the auxiliary field method, is a technique to obtain approximate solutions of N -body Hamiltonians in quantum mechanics [1,2]
The method is easy to implement since it reduces to find the solution of a transcendental equation
Better results are obtained for mean values, for which an integration is performed with the density over the whole domain of distances
Summary
The envelope theory (ET), known as the auxiliary field method, is a technique to obtain approximate solutions of N -body Hamiltonians in quantum mechanics [1,2]. In the most favourable cases, the approximate eigenvalue is an analytical lower or upper bound. A nonvariational numerical approximation can be computed. This is often interesting for N -body problems which are always difficult and very heavy to solve numerically. It has been shown that the approximation given by the ET can be largely improved by modifying the structure of the characteristic global quantum number of the method [7,8]. The ET method is recalled, where a modification of the global quantum number is proposed to improve the quality of the approximation.
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