Classical equivalents of one-dimensional quantum-mechanical systems

1978 ◽  
Vol 18 (7) ◽  
pp. 3351-3359 ◽  
Author(s):  
Mustansir Barma ◽  
B. Sriram Shastry
Keyword(s):  
Mechanical Systems ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Quantum Mechanical Systems

scholarly journals Consequences of deformation of the Heisenberg algebra

2015 ◽  
Vol 12 (02) ◽  
pp. 1550022 ◽  
Author(s):  
Mir Faizal
Keyword(s):  
Gauge Symmetry ◽  
Mechanical Systems ◽  
Heisenberg Algebra ◽  
Dimensional Case ◽  
Quantum Mechanical ◽  
Second Quantization ◽  
One Dimensional ◽  
Non Local ◽  
Quantum Mechanical Systems

In this paper, we will demonstrate that like the existence of a minimum measurable length, the existence of a maximum measurable momentum, also influence all quantum mechanical systems. Beyond the simple one-dimensional case, the existence of a maximum momentum will induce non-local corrections to the first quantized Hamiltonian. However, these non-local corrections can be effectively treated as local corrections by using the theory of harmonic extensions of functions. We will also analyze the second quantization of this deformed first quantized theory. Finally, we will analyze the gauge symmetry corresponding to this deformed theory.

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