Linked Questions
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Why do you need symmetric and antisymmetric solutions of the time-independent Schrödinger Equation by a given potential $V(x)$? [duplicate]
I've calculated many symmetric and antisymmetric solutions of the time-independent Schrödinger Euqation by a given square potentials $V(x)$. Just for practice etc., but honestly I do not understand ...
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Schrodinger equation: If $V(x)=V(-x)$ then prove that $\psi(x)=\psi(-x) $ or $\psi(x)=-\psi(-x)$ [duplicate]
The title explains itself. If the potential is an even function then prove that wave function is either odd or even. I set $-x$ in Schrodinger equation and find out that $\psi(-x)$ is also a solution ...
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Solutions to time-independent Schrödinger's equation with symmetrical (even) potential [duplicate]
A problem from Griffith's Introduction to Quantum Mechanics asks to prove the following:
Given a symmetric potential $V(x)$ $(=V(-x))$, the solutions to the time-independent Schrödinger's equation ...
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Missing parity of free particle [duplicate]
in this Definite Parity of Solutions to a Schrödinger Equation with even Potential? post in David Z's answer it's stated that the eigenfunctions have parity if the potential has parity/if $[H,P]=...
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Definite Parity of Solutions to a Schrödinger Equation with even Potential?
I am reading up on the Schrödinger equation and I quote:
Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity.
Could someone kindly explain ...
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When Eigenfunctions/Wavefunctions are real?
When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real?
What happens in 1D case like the finite ...
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Solving the time independent Schrodinger equation: Does a complex solution make sense?
In my notes, I have the Time Independent Schrodinger equation for a free particle
$$\frac{\partial^2 \psi}{\partial x^2}+\frac{p^2}{\hbar^2}\psi=0\tag1$$
The solution to this is given, in my notes, ...
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What is "definite parity" in quantum mechanics?
I am studying for an exam on quantum mechanics, and have come across something which I don't understand. The problem is:
We have a symmetric potential, i.e. $V(x)=V(-x)$. If the energy eigenvalue ...
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Derivation of the "Bethe sum rule"
I am trying to work out the steps of the proof of the expression: $$\sum_n (\mathcal{E_n}-\mathcal{E_s})|\langle n|e^{i\mathbf{q}\cdot\mathbf{r}}|s \rangle|^2 = \frac{\hbar^2q^2}{2m}$$ from Eq. (5.48) ...
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Why the hydrogen radial wave function is real?
Why the hydrogen radial wave function is real?
Is it a coincidence?
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Wavefunction restrictions of odd potentials
So I was just reading back through Griffiths' "Introduction to Quantum Mechanics" and solving some of the problems for practice. There is a nice one (problem 2.1c for those playing at home) where you ...
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Bound state in a potential well?
Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html
It says:
This means that the solutions separate into even parity and odd parity states. We could have guessed this from ...
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Parity in the Double Delta-Function Potential
I'm working through Griffith's Intro to Quantum Mechanics, attempting to solve problem 2.27.
Consider the double delta-function potential $$ V(x)= -\alpha [\delta(x+a)+\delta(x-a)] $$ where $\alpha$ ...
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Finite potential well, parity of solutions
I'm working through some problems for a QM exam and I've realised I don't really understand the concept of parity of solutions. I'm looking at a simple finite potential well problem: $$V(x)=0, \quad |...
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Stationary state of time-independent Schroedinger equation is always real valued function?
I am reflecting on the solution of the time-independent Schroedinger equation.
My reasoning is that the stationary state of the time-independent Schroedinger equation must be a real valued function ...
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