spin example of tensor product
DOCX · 18.2 KB
Open DOCX file
A brief fragment in Phil's Wedge World tensor notes, dated about 1.11.15 and built on a blank template. It explains that two particles of spin s and s' have states |s,m>|s',m'> spanning (2s+1)-dimensional spaces, whose tensor product is often called a direct product. It links this to representations of the rotation group, then begins to write the two-particle state as |ψ(1)>|ψ(2)>. The text breaks off.
AI-written summary; may contain errors. This description is approximate.
Extracted text (machine-read; may contain errors)
This is the Title PhL 1.11.15
Note that page numbering is turned on in this template and view is 125%,
located in phil/roaming/microsoft/templates size about 219K.
(4) In physics, a quantum state of two particles of spin s and s' can be written |s,m> |s',m'> where the state vectors |s,m> with m = s,s-1..-s span a vector space of dimension (2s+1). In this context, one has a tensor product space SS'. This space is often referred to, however, as a direct product space. The states written as |s,m> span a finite dimensional representation of the rotation group, so there is a connection with "groups". One can regard S and S' as if they were two different groups (representations of the same group) and then the direct product term has more justification.
the tensor product of the quantum states (state vectors) of two particles is written |ψ(1)> |ψ(2)> and