Graduate Quantum Mechanic/wave function/junction condition

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To eliminate constants C and D and derive the last two equations, it's essential to clarify the intermediate steps between the 4th and 5th equations, as some calculations appear to be omitted. Verifying the algebra is crucial, as trusting the author's work without checking may lead to errors. Providing context for the boundary condition equations and the wave numbers k_i, k_i', and k_i'' is necessary for a comprehensive understanding. The discussion emphasizes the importance of thoroughness in calculations, likening it to the unpleasantness of eating oatmeal, which ultimately leads to easier problem-solving later. Clear communication of these steps will benefit readers seeking to grasp the underlying concepts.
GreenTea09
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May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?
 
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It looks like quite a few steps have been skipped. You either trust the author or check the algebra yourself.
 
Or the best of both worlds: trust, but verify. Doing a messy calculation is like eating oatmeal, not pleasant in the moment but makes things easier later.
 
And for the sake of PF readers: provide essential context so we can see where these boundary condition equations are sitting ! And where the wave number is ##k_i, k_i', k_i''## (hey, can we skip the subscript 1 ?
 

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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