What are the key applications of Relativistic corrections in modern physics?

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Relativistic corrections are essential in various fields of physics, particularly in accurately calculating the band structure of materials, including conductors, semiconductors, and insulators. These corrections are crucial for understanding phenomena that occur at high velocities, where classical physics fails to provide accurate predictions. Technologies such as GPS and particle accelerators also rely on relativistic corrections to ensure precise functionality. The necessity of these corrections arises from the effects of high-speed particles and the influence of gravity on time and space. Overall, relativistic corrections play a vital role in both theoretical physics and practical applications.
taoke
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I had a few questions about Relativistic correction:

A. Where in physics are Relativistic corrections made? and why?

B. What are some examples of technologies that must apply Relativistic corrections? why?
 
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taoke said:
I had a few questions about Relativistic correction:

A. Where in physics are Relativistic corrections made? and why?

B. What are some examples of technologies that must apply Relativistic corrections? why?

Many areas of physics use the reletivistic correction. An example where you might not think it is necessary is in the correct calculation of the band structure of material whether it be a conductor, semiconductor or insulator.
 

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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