The T-matrix, whose precise definition must be given somewhere else in the book, can be expanded into a power series in the coupling strength g. The zeroth- order term is trivial, as it corresponds to no scattering at all. The term containing the lowest non-vanishing power of g (g^1 in this example) is the leading order.Bin Jiang said:Summary:: How to understand T-matrix in two-body scattering? Especially how to understand "leading order" in the text.
How can we understand T-matrix in two-body scattering? Especially term "leading order" in the text. In addition, how to understand the connection between fig2.3 and equation 2.24-2.26?
Thanks.
The T-matrix is a mathematical tool used to describe the scattering of two particles in quantum mechanics. It relates the incoming and outgoing states of the particles and contains information about the interaction between them.
The T-matrix is typically calculated using perturbation theory, where the interaction between the particles is treated as a small perturbation to the free particle states. This allows for the T-matrix to be expressed as a series expansion in terms of the interaction strength.
The T-matrix is a fundamental quantity in understanding the scattering process between two particles. It can be used to calculate various properties such as cross sections and scattering amplitudes, which are important in experimental measurements and theoretical predictions.
The T-matrix can vary depending on the type of scattering being studied. For example, in elastic scattering, where the particles maintain their identity after the interaction, the T-matrix is a unitary operator. In inelastic scattering, where the particles can change their identity, the T-matrix is non-unitary.
The T-matrix has many applications in various fields of physics, such as nuclear physics, particle physics, and atomic and molecular physics. It is used to study scattering processes in these systems and can provide insights into the underlying interactions between particles. Additionally, the T-matrix is also used in quantum field theory to calculate scattering amplitudes in high energy physics experiments.