29 questions linked to/from Are all scattering states un-normalizable?
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### What is the scope of the term 'normalisation'?

When we 'normalise' the wavefunction we put in an appropriate coefficient so that the wavefunction can act as a probability distribution. However, when I considered the eignefunctions of the momentum ...
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### Eigenfunctions of observables

Are eigenfunctions of observables solutions to the time-dependent Schrödinger equation? Or is this not necessarily the case? From what I had been reading they are not necessarily solutions to ...
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### Probability of finding an energy state of a non-normalisable wave-function

Suppose, say, I have the following wave function It represents the wave function of a free particle. I would want to calculate the probability of finding the particle with energy ħk and energy 2ħk. ...
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I am trying to do problem 2.4 in the book "Quantum field theory for the gifted amateur". I have a math background but little training in physics. I am asked to use the identity $$\langle x \mid p \... 1answer 224 views ### Bras and kets of continuous spectrum Does anyone know why in quantum mechanics the second statement is always true? "When the spectrum of an operator A has a continuous part, we associate a bra \langle a| and a ket |a \rangle ... 1answer 326 views ### Protocol for solving time independent Schrodinger equation Just a short question about the protocol for solving the time-independent Schrodinger equation for different potentials and the reasons for accepting and rejecting solutions. Take for example the ... 1answer 215 views ### Is it possible to decompose into eigenstates of Dirac Hamiltonian? If we have the Hilbert space \mathcal H = L^2(\mathbb R^3, \mathbb C^4) and a Hamiltonian:$$H=\gamma^i p_i + m \gamma^0$$where \gamma^i are matrices and \{\gamma^i,\gamma^j\}=\delta^{ij}. A ... 2answers 432 views ### Can a normalizable function *always* be decompose into the discrete Hydrogen spectrum? This question has been bothering me for a while now: can one reconstruct an arbitrary (normalizable) function \phi(\mathbf r) in \mathbb R^3, with only the (discrete) set of Hydrogen ... 2answers 920 views ### Must bounded operators have normalisable eigenfunctions and discrete eigenvalues? When we have bound states, to my knowledge, we have states that are normalisable and a discrete energy spectrum. However, in the case of scattering states that have a continuous energy spectrum, the ... 3answers 3k views ### What really is a Dirac delta function? Yesterday a friend asked me what a Dirac delta function really is. I tried to explain it but eventually confused myself. It seems that a Dirac delta is defined as a function that satisfies these ... 1answer 838 views ### Continuous spectrum of hydrogen atom I wonder if there is a nice treatment of the continuous spectrum of hydrogen atom in the physics literature--showing how the spectrum decomposition looks and how to derive it. 2answers 1k views ### Does a free electron, one that's not either in an atom or a wire, have an associated wave-function? Would a free electron, one that's not either in an atom or moving through a wire, but moving through empty space on its own, have an associated wave-function? Or, is an electron described as a wave-... 2answers 1k views ### How to guarantee square integrable solutions to time-independent Schrödinger's equation? Given the time-independent Schrödinger’s equation in one dimension$$H\psi = E\psi what restrictions can we place on V(x) (inside the hamiltonian) and E to guarantee that the solutions won't have ...
I would like first to describe a strange case that I encountered. $\ \ -$ I solved the Schrodinger equation with a potential barrier (a potential well limited by a finite height wall which decrease ...