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What is the difference between Dirac's delta function and the Kronecker delta function?

It seems to me they are related only in name. The Kronecker delta is just a function of two variables that is 1 if they are equal and 0 if they are not. The Dirac delta function is a mathmatical construct to help us solve some problems

To expand on Dark Helmet's answer, the Dirac delta function is a function that is zero everywhere except at δ(0), where it is infinite. The integral of a Dirac delta function is always 1 (provided that the integral includes δ(0)). The Kronecker delta is most useful when defining orthonormality–whenever m≠n, the inner product of two eigenfunctions is zero; whenever m=n, the inner product is 1 (provided the functions are normalized).

What is a determinate state?

 As far as I can tell, determinate states are just eigenfunctions of certain operators.  For example, the stationary states we've been studying are determinate states of the Hamiltonian.  For the stationary states, every measurement of the particle in a stationary state gives a corresponding energy.  It really is just eigenfunctions and eigenvalues.

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