| Título: | Brackets de transformación para funciones de oscilador armónico |
| Autores: | BRODY , TOMÁS |
| Fecha: | 1969-12-31 |
| Publicador: | Revista Mexicana de Física |
| Fuente: |
Ver documento |
| Tipo: | |
| Tema: | No aplica |
| Descripción: |
THE USEFULNESS OF THE SHELL MODEL IS GREATLY BY THE POSSIBILITY, RECENTLY DEVELOPED BY MOSHINSKY, OF EXPRESSING TWO-NUCLEON MATRIX ELEMENTS DIRECTLY IN TERMS OF TALMI INTEGRALS BY MEANS OF TRANSFORMATION BRACKETS CONNECTING THE TWO-NUCLEON WAVE-FUNCTIONS WITH THE CENTRE-OF-MASS AN RELATIVE COORDINATE WAVE-FUNCTIONS. I- N1,N2; I1, I2 ARE THE RADIAL AND ANGULAR MOMENTUM QUANTUM NUMBERS OF THE TWO PARTICLE, MOVING IN A COMMON POTENTIAL TAKEN AS THAT OF THE HARMONIC OSCILLATOR, AND N, L; N, I ARE THE CORRESPONDING QUANTUM NUMBERS IN THE CENTRE-OF-MASS AND RELATIVE COORDINATE REPRESENTATION, WHILE - IS THE TOTAL ANGULAR MOMENTUM, THE TRANSFORMATION BRACKET IS WRITTEN AS ______________ . FOR N1 = N2 = 0 A CLOSED EXPRESSION IS GIVEN BY (3) AND (4) OF THE TEXT, AND IN TABLE 2 THE NUMERICAL VALUES OF THESE PARTICULAR TRANSFORMATION BRACKETS ARE GIVEN FOR ________________ . THE VALUES ARE GROUPED IN 140 GROUPS ACCORDING TO THE VALUES OF _____ AND __, WICH ARE GIVEN AT THE BEGINNING OF EACH GROUP IN THE FIRST COLUMNS IN THAT ORDER. THE NEXT FOUR COLUMNS GIVE THE VALUE OF __________________ FOR THE GROUP, AND THE FOLLOWING CULUMN SHOWS THE NUMERICAL VALUE OF THE TRANSFORMATION BRACKET _______________ . IN THE LAST COLUMN THE NUMBER __ OF TRANSFORMATION BRACKETS IN THE GROUP IS GIVEN AT THE END. __ IS GIVEN BY THE RELATIONS (20) OF THE TEXT. THE TRANSFORMATION BRACKETS OBEY THE ORTHONORMALITY RELATION (17), SO THAT THE SUN OF THE SQUARES OF THE VALUES IN EACH GROUP SHOULD BE I. THIS HAS BEEN CHECKED FOR ALL 140 GROUPS, AS HAS THE ORTHOGONALITY OF A NUMBER OF PAIRS OF GROUPS WITH EQUAL __ AND __ BUT DIFFERENT __ AND __. DUE TO THE COMULATION OF ROUNDING-OFF ERRORS, THE LAST DECIMAL OF THE NUMERICAL VALUES IN THE TABLES MAY BE IN ERROR BY SEVERAL UNITS. THE ROOT-MEAN-SQUARE DERIVATION FROM THE CORRECT VALUES, OBTAINED FROM THE NORMALITY CHECK, IS 2.9 UNITS IN THE LAST DECIMAL, SO THAT THE SEVENTH DECIMAL MAY BE TAKEN AS CORRECT ALMOST ALL CASES. A LIST IS GIVEN (TABLE 1) OF THOSE GROUPS FOR WICH THE SUN OF THE SQUARES DIFFERS BY MORE THAN 5 X 10- FROM1. NO ROUNDING OFF BY HAND WAS ATTEMPTED. EXPLICIT FORMULAE FOR THE USE OF THESE TRANSFORMATION BRACKETS IN CALCULATING SHELL-MODEL MATRIX ELEMENTS, AS WELL AS SOME SUPPLEMENTARY TABLES, WILL BE FOUND IN ANOTHER PAPER. THE USEFULNESS OF THE SHELL MODEL IS GREATLY BY THE POSSIBILITY, RECENTLY DEVELOPED BY MOSHINSKY, OF EXPRESSING TWO-NUCLEON MATRIX ELEMENTS DIRECTLY IN TERMS OF TALMI INTEGRALS BY MEANS OF TRANSFORMATION BRACKETS CONNECTING THE TWO-NUCLEON WAVE-FUNCTIONS WITH THE CENTRE-OF-MASS AN RELATIVE COORDINATE WAVE-FUNCTIONS. I- N1,N2; I1, I2 ARE THE RADIAL AND ANGULAR MOMENTUM QUANTUM NUMBERS OF THE TWO PARTICLE, MOVING IN A COMMON POTENTIAL TAKEN AS THAT OF THE HARMONIC OSCILLATOR, AND N, L; N, I ARE THE CORRESPONDING QUANTUM NUMBERS IN THE CENTRE-OF-MASS AND RELATIVE COORDINATE REPRESENTATION, WHILE - IS THE TOTAL ANGULAR MOMENTUM, THE TRANSFORMATION BRACKET IS WRITTEN AS ______________ . FOR N1 = N2 = 0 A CLOSED EXPRESSION IS GIVEN BY (3) AND (4) OF THE TEXT, AND IN TABLE 2 THE NUMERICAL VALUES OF THESE PARTICULAR TRANSFORMATION BRACKETS ARE GIVEN FOR ________________ . THE VALUES ARE GROUPED IN 140 GROUPS ACCORDING TO THE VALUES OF _____ AND __, WICH ARE GIVEN AT THE BEGINNING OF EACH GROUP IN THE FIRST COLUMNS IN THAT ORDER. THE NEXT FOUR COLUMNS GIVE THE VALUE OF __________________ FOR THE GROUP, AND THE FOLLOWING CULUMN SHOWS THE NUMERICAL VALUE OF THE TRANSFORMATION BRACKET _______________ . IN THE LAST COLUMN THE NUMBER __ OF TRANSFORMATION BRACKETS IN THE GROUP IS GIVEN AT THE END. __ IS GIVEN BY THE RELATIONS (20) OF THE TEXT. THE TRANSFORMATION BRACKETS OBEY THE ORTHONORMALITY RELATION (17), SO THAT THE SUN OF THE SQUARES OF THE VALUES IN EACH GROUP SHOULD BE I. THIS HAS BEEN CHECKED FOR ALL 140 GROUPS, AS HAS THE ORTHOGONALITY OF A NUMBER OF PAIRS OF GROUPS WITH EQUAL __ AND __ BUT DIFFERENT __ AND __. DUE TO THE COMULATION OF ROUNDING-OFF ERRORS, THE LAST DECIMAL OF THE NUMERICAL VALUES IN THE TABLES MAY BE IN ERROR BY SEVERAL UNITS. THE ROOT-MEAN-SQUARE DERIVATION FROM THE CORRECT VALUES, OBTAINED FROM THE NORMALITY CHECK, IS 2.9 UNITS IN THE LAST DECIMAL, SO THAT THE SEVENTH DECIMAL MAY BE TAKEN AS CORRECT ALMOST ALL CASES. A LIST IS GIVEN (TABLE 1) OF THOSE GROUPS FOR WICH THE SUN OF THE SQUARES DIFFERS BY MORE THAN 5 X 10- FROM1. NO ROUNDING OFF BY HAND WAS ATTEMPTED. EXPLICIT FORMULAE FOR THE USE OF THESE TRANSFORMATION BRACKETS IN CALCULATING SHELL-MODEL MATRIX ELEMENTS, AS WELL AS SOME SUPPLEMENTARY TABLES, WILL BE FOUND IN ANOTHER PAPER. |
| Idioma: | Español |
1 Ordered Hunt Schemes for Overlaid CDMA Cellular Systems,Esquemas de ordenamiento en sistemas celulares sobrepuestos CDMA por Castañeda Camacho, J; Benemérita Universidad Autónoma de Puebla, Puebla, México,Lara Rodríguez, D; IPN | 6 Model for Adjustment of Aggregate Forecasts using Fuzzy Logic,Modelo para el ajuste de pronósticos agregados utilizando lógica difusa por Escobar Gómez, E N; Instituto Tecnológico de Tuxtla Gutiérrez Chiapas,Díaz Núñez, J J; Universidad Autónoma de Ciudad Juárez Chihuahua,Taracena Sanz, L F; Instituto Tecnológico de Querétaro, Querétaro |
2 Volatile Organic Compound Emissions from Light-Duty Vehicles During Cold-Starts,Emisiones de compuestos orgánicos volátiles durante arranques en frío de automóviles ligeros por Mendoza Domínguez, A; Tecnológico de Monterrey, Campus Monterrey, Nuevo León, México,León Romero, M A; Tecnológico de Monterrey, Campus Monterrey, Nuevo León, México,Caballero Mata, P | 7 Matrix Formulation of Foundations for Vibrating Machinery in Frequency Domain,Formulación matricial de cimentaciones para maquinaria vibratoria en el dominio de la frecuencia por Carbajal Romero, M F; Instituto Politécnico Nacional. México DF,Rodríguez Castellanos, A; Instituto Mexicano del Petróleo. México DF,Rodríguez Sánchez, J E; Instituto Mexicano del Petróleo. México DF,Flores Méndez, E; IPN |
3 Hydrogen Sorption Properties of the Intermetallic Mg2Ni Obtained by Using a Simoloyer Ball Milling,Propiedades de ab-desorción de hidrógeno del intermetálico Mg2Ni obtenido empleando un molino de bolas Simoloyer por Martínez Franco, E; IPN,Klassen, T; GKSS, Research Center Geesthacht, Germany,Jaramillo Vigueras, D; IPN,Bormann, R; GKSS, Research Center Geesthacht, Germany | 8 Numerical Approach to an Outflow Hydrograph of a Dambreak,Estimación numérica del hidrograma de salida de una presa debido a su ruptura por Fuentes Mariles, O A; Universidad Nacional Autónoma de México,Arganis Juárez, M L; UNAM,De Luna Cruz, F; UNAM,Franco, V; UNAM |
4 Electrical Parameters Extraction of CMOS Floating-Gate Inverters,Extracción de parámetros eléctricos de inversores CMOS de compuerta flotante por Molinar Solís, J E; Universidad Autónoma del Estado de México,Ponce Ponce, V H; IPN,García Lozano, R Z; Universidad Autónoma del Estado de México,Díaz Sanchez, A; Instituto Nacional de Astrofísica, Óptica y Electrónica INAOE,Rocha Pérez, j M; Instituto Nacional de Astrofísica, Óptica y Electrónica INAOE | 9 Back Work Ratio of Brayton Cycle,La relación de trabajo de retroceso de un ciclo Brayton por Malaver de la Fuente, M; Universidad Marítima del Caribe, Venezuela |
5 Active Rectifier with Extended Functions: An Option to Voltage Sags Ride Through and Power Quality Improvement,Rectificador activo con funciones ampliadas: una alternativa para la compensación de sags de voltaje y mejorar la calidad de la red eléctrica por Núñez Gutiérrez, C A; Universidad Autónoma de San Luis Potosí, SLP,Lira Pérez, J; Universidad Autónoma de San Luis Potosí, SLP,Pazos Flores, F; Universidad Autónoma de San Luis Potosí, SLP,Echavarría Solís, R; Universidad Politécnica de Victoria, Ciudad Victoria, Tamaulipas | 10 Flood Predictions Combining Regional and Single Site Hydrometric Information,Predicción de crecientes combinando información hidrométrica local y regional por Campos Aranda, D F; Universidad Autónoma de San Luis Potosí |