The exact solution for a forced, undamped quantum harmonic oscillator is obtained by S-matrix techniques. The force F(t) is assumed to vanish at t = ±∞. The only restriction is that the Fourier transform of F(t) must exist. The transition probabilities are obtained in closed form in terms of Laguerre polynomials. The mean energy transfer to the oscillator is found to be independent of the initial state and is in agreement with the classical result for an oscillator originally at rest. This problem provides a good example of field theoretical procedures in an elementary context. Therefore, all field theoretical concepts are carefully defined and explained as they are introduced in order that the discussion may be self-contained.
The asymptotic properties of a Schrodinger wave function which represents the bound ground state of a system of three interacting particles are examined. It is assumed that the interaction can be described by a static potential which is the sum of three two-body potentials and one three-body potential, where the potentials have the property that if any one of the particles is separated from the other two by a distance which tends to infinity, then the part of the potential energy which depends on the position of that particle tends to zero. The problem is treated nonrelativistically. Decreasing exponential bounds on the ground-state three-body wave function are established in configuration space. It is shown that these bounds depend only on the masses of the three particles, on the ground-state energy of the three-body system, and on the lower bounds on the spectra of the Hamiltonians for the three two-body systems arising when one of the three particles is removed and the remaining two interact through
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DISCLAIMERThe work is formulated in t e r m s of S y m m e t r i c finite strain p a r a m e t e r s and a p p r o p r i a t e i n t e r n a l s t r a i n s a r e introduced i n such a m a n n e r that the f o r m u l a t i o n exhibits explicitly the invariance of the c r y s t a l potential e n e r g y and n o r m a l mode frequencies to r i g i d body r o t a t i o n s . As a n u m e r i c a l app:lication t h e coefficient of l i n e a r . expansion and the phonon frequency distributions a t 300°K and 800°K have . been calculated f o r z i r c o n i u m hydride with a s h o r t -r a n g e c e n t r a l f o r c e model including third -n e a r e s t -neighbor f o r c e s .
5. i i CONTENTS
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