Linked Questions

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1 answer
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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 ...
physics's user avatar
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1 answer
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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 ...
lifeistod's user avatar
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0 answers
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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 ...
Sidd's user avatar
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0 answers
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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]=...
peter mafai's user avatar
32 votes
3 answers
40k views

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 ...
bra-ket's user avatar
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18 votes
2 answers
12k views

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 ...
Lorniper's user avatar
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5 votes
1 answer
7k views

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, ...
Joebevo's user avatar
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3 votes
1 answer
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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 ...
John Doe's user avatar
  • 491
12 votes
3 answers
2k views

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) ...
PhHEP's user avatar
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3 votes
3 answers
1k views

Why the hydrogen radial wave function is real?

Why the hydrogen radial wave function is real? Is it a coincidence?
Arnaud's user avatar
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0 votes
2 answers
3k views

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 ...
Lachy's user avatar
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1 vote
1 answer
2k views

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 |...
Spine Feast's user avatar
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0 votes
1 answer
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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 $\alpha$ ...
NoVa's user avatar
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1 vote
2 answers
2k views

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 ...
Outrageous's user avatar
1 vote
2 answers
1k views

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 ...
Chaos's user avatar
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