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A linear potential plus a constrained Fermi-Breit gluon-exchange interaction is used in a nucleon-structure calculation. The potential-strength parameters are adjusted to fit the proton charge form factor. A range of strength parameters that are consistent with the experimental proton charge form factor is given. The corresponding excited-nucleon spectrum due to the linear potentials is also calculated. The results are generally consistent with previous calculations by other authors using similar Hamiltonians and also with the experimental data considered. The spatially symmetric S-state quark wave functions are obtained by a variational method. The accuracy of the variational wave function is tested with the harmonic-oscillator Hamiltonian which possesses exact solutions.

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