How do complex numbers manifest themselves in the subatomic world?

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Complex numbers are essential in quantum mechanics, serving as a fundamental tool for describing the behavior of elementary particles. They also play a crucial role in wave mechanics, highlighting their significance in understanding natural phenomena. The discussion suggests that without complex numbers or geometric algebra, the description of subatomic particles would be incomplete. This underscores the deep connection between mathematics and the physical world at the quantum level. Overall, complex numbers are integral to the framework of modern physics.
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Im am very curios as to what role complex numbers might have in nature?
 
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They play a huge role in quantum mechanics. They also are fundamental for describing waves in general.
Elementary particles cannot be described without complex numbers (or something like geometric algebra where the behavior of the complex numbers are described using geometrical structures).
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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