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The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case. Resumo. O problema de uma partícula de spin 1/2 confinada por uma caixa a uma dimensãoé resolvido de uma maneira muito semelhanteà da resolução do problema de uma partícula no-relativista numa caixa referido em muitos livros introdutórios de Mecânica Quntâica. Os níveis de energia e a densidade de probabilidade são calculados e comparados com os valores não-relativistas.

Explicit functions are widely used to interpolate, extrapolate, and differentiate theoretical or experimental data on the equation of state ͑EOS͒ of a solid. We present two EOS functions which are theoretically motivated. The simplest realistic model for a simple metal, the stabilized jellium ͑SJ͒ or structureless pseudopotential model, is the paradigm for our SJEOS. A simple metal with exponentially overlapped ion cores is the paradigm for an augmented version ͑ASJEOS͒ of the SJEOS. For the three solids tested ͑Al, Li, Mo͒, the ASJEOS matches all-electron calculations better than prior equations of state. Like most of the prior EOS's, the ASJEOS predicts pressure P as a function of compressed volume v from only a few equilibrium inputs: the volume v 0 , the bulk modulus B 0 , and its pressure derivative B 1. Under expansion, the cohesive energy serves as another input. A further advantage of the new equation of state is that these equilibrium properties other than v 0 may be found by linear fitting methods. The SJEOS can be used to correct B 0 and the EOS found from an approximate density functional, if the corresponding error in v 0 is known. We also ͑a͒ estimate the typically small contribution of phonon zero-point vibration to the EOS, ͑b͒ find that the physical hardness Bv does not maximize at equilibrium, and ͑c͒ show that the ''ideal metal'' of Shore and Rose is the zero-valence limit of stabilized jellium.