Studio portrait of David Dublon; Simmern (Simmertal), Germany Portraits Men

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Studio portrait of David Dublon; Sülzhayn, Germany Portraits Men

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Interior view of the synagogue where David Dublon was cantor or rabbi; Dülmen, Germany Synagogues; Interior

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Interior view of the synagogue where David Dublon was cantor or rabbi with some of the children in the congregation; Dülmen, Germany Synagogues; Interior

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Studio portrait of Fritz Loewenthal at about six years old; Teschen, Germany.

Teschen, Germany or Cieszyn, Poland or Český Těšín, Czech Republic

Herman Sommerfeld (fifth from right) with other soldier recruits; Döberitz, Germany Portraits Men

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Fred Herz seated on a car hood on a country road; Harzfahrt (Harz Mountains), Germany.

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Schoenewald family portrait; Bad Nauheim, Germany.

Includes Rosi Schoenewald (sister of Dora), Dora Schoenewald (wife of Alfred Apfel and mother of Hannah Busoni), Henni Apfel, Tilly Schoenewald, Luise Schoenewald, Max Schoenewald (brother of Dora), Felix Schoenewald (brother of Dora), Samuel Schoenewald (brother of Dora), and Gerhardt Schoenewald

Officer guards and inmates, including Norbert Pollock, of the Boergermoor Labor Camp; Germany.

Viehhandler (cattle dealer) Norbert Pollock of Ruethen, Westpflahlen (standing center in dark pants, white t-shirt and cap)

Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Elly, Dorothea, Leopold, Klaus and Ruth on vacation near the sea; Heringsdorf, Germany.

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