Understanding the Role of the Quantization Axis in Angular Momentum Measurements

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The quantization axis is a reference direction chosen for measuring angular momentum, typically designated as the z-axis. This choice allows for the angular momentum components to be expressed in a basis where the z-component has well-defined values, known as eigenstates of the \hat{J}_z operator. Authors often simplify this concept by stating that the z-axis is the quantization axis without delving into its implications. Understanding this axis is crucial for accurately interpreting angular momentum measurements in quantum mechanics. The quantization axis fundamentally influences the outcomes of these measurements.
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What is quantisation axis? In many books authors just say that we choose that z is quantization axis.
 
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This is just saying that you consider everything in a basis, where the [itez]z[/itex] components of angular momenta have well-determined values (eigenstates of the corresponding \hat{J}_z operators).
 

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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