Angular Momentum Techniques in Quantum Mechanics

Fungamwango Hashel Mwansa, Phillippe Kabwita

This study aimed at investigating the problems students face in understanding the concepts of angular momentum in classical and quantum mechanics, finding an effective way of improving understanding and learning the concepts of angular momentum in quantum mechanics, lastly document the challenges investigated and suggest some solutions to help students understand angular momentum in both classical and quantum mechanics. This study summarizes a series of investigations into how undergraduate Physics students perceive angular momentum in quantum mechanics at the University of Zambia. We investigated undergraduate physics student's perception of angular momentum in quantum mechanics by administering written questions (open-ended) to two different groups of classes. Out of these investigations we developed a Quantum Interactive Learning Tutorials (Qu I L Ts) and peer instruction tools to assist the students build up a considerable knowledge structure of quantum mechanics in general and angular momentum in specific, through a guided approach technique [1]. Eleven questions were administered to a group of N = 15 students, statistics for answered questions are as follows; question one 4 out of 15 representing a percentage of 26.67%, question two only 6 out of 15 student representing 40%, question three 11 out of 15 representing a percentage of 73.33%, for question four only 1 out of 15 representing a percentage of 6.67%, question five none of the students answered, question six only 1 out of 15 students representing a percentage of 6.67% managed to answer, question seven 1 out of 15 representing a percentage of 6.67% managed to answer, question eight 11 out of 15 representing a percentage of 73.33 % got the correct answer, question nine 6 out of 15 representing a percentage 40% got the right answer, question ten only three students making a percentage of 20% answered correctly, question eleven no student managed to get it right. Preliminary results show that the undergraduate physics students perception of quantum mechanics is improved after using the research-based learning tools in the lower class level quantum mechanics courses [1]. We also build up a common conceptual survey that can help lecturers better investigate undergraduate physics students understand the concept of angular momentum in particular and quantum mechanics courses in general.

David V. George

Sri Purwaningsih, Febri Berthalita Pujaningsih, Neneng Lestari +1 more

Angular momentum can simply be interpreted as the momentum of an object that rotates or rotates. Angular momentum or angular center intuitively measures how much linear momentum is directed around a certain point or often called the center point. In this paper, an analysis of angular momentum in quantum mechanics has been carried out, as well as a study of the expansion of the application of angular momentum in quantum mechanics in the form of the Clebsch–Gordan coefficient.

Walter Kauzmann

László B. Szabados

Complex and spinorial techniques of general relativity are used to determine all the states of SU(2) invariant quantum mechanical systems in which the equality holds in uncertainty relations for the components of the angular momentum vector operator in two given directions. The expectation values depend on a discrete quantum number and two parameters, one of them is the angle between two angular momentum components and the other is the quotient of two standard deviations. Allowing the angle between two angular momentum components to be arbitrary, a new genuine quantum mechanical phenomenon emerges: it is shown that although standard deviations change continuously, one of the expectation values changes discontinuously on this parameter space. Since physically neither of the angular momentum components is distinguished over the other, this discontinuity suggests that the genuine parameter space must be a double cover of this classical one: it must be diffeomorphic to a Riemann surface known in connection with the complex function z. Moreover, the angle between angular momentum components plays the role of the parameter of an interpolation between the continuous range of expectation values in the special case of orthogonal angular momentum components and the discrete point spectrum of one angular momentum component. The consequences in the simultaneous measurements of these angular momentum components are also discussed briefly.

K. Heyde