A new derivation of quantum‐mechanical angular momentum operator L2

1976 ◽  
Vol 44 (9) ◽  
pp. 888-889
Author(s):  
P. D. Gupta
Keyword(s):  
Angular Momentum ◽  
Momentum Operator ◽  
Quantum Mechanical ◽  
Angular Momentum Operator

scholarly journals GLUEBALL SPIN

2001 ◽  
Vol 16 (01) ◽  
pp. 41-51
Author(s):  
D. SINGLETON
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Momentum Operator ◽  
Angular Momentum Operator ◽  
Total Field ◽  
Expectation Value ◽  
Starting Point ◽  
Simplifying Assumptions

The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is re-examined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the possible restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationships. This analysis can be compared to the electromagnetic charge/monopole system, where the requirement that the total field angular momentum obey the angular momentum commutation relationships places restrictions (i.e. the Dirac condition) on the system. Second, we look at the expectation value of the field angular momentum operator under some simplifying assumptions.

scholarly journals SWKB for the Angular Momentum

1997 ◽  
Vol 11 (18) ◽  
pp. 801-805 ◽  
Author(s):  
Luca Salasnich ◽  
Fabio Sattin
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Eigenvalue Problem ◽  
Momentum Operator ◽  
Angular Momentum Operator ◽  
Leading Order

It has been recently shown [M. Robnik and L. Salasnich, J. Phys. A: Math. Gen.30, 1719 (1997)] that the WKB series for the quantization of angular momentum L converges to the exact value L2=ℏ2l(l+1), if summed over all orders, and gives the Langer formula L2=ℏ2(l+1/2)2 at the leading order. In this work we solve the eigenvalue problem of the angular momentum operator by using the supersymmetric semiclassical quantum mechanics (SWKB), and show that it gives the correct quantization already at the leading order.

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