Particle in a box 2

In A Particle in a Box- 1 we have seen that we can write the quantum state of a particle in a box in the eigen-basis of energy operator. From now on we will call this the Hamiltonian operator. For a recap the eigenvalue equation for the Hamiltonian for a particle in a box system is

$latex \hat H \left| \phi_n\right\rangle = E_n \left|\phi_n\right\rangle&s=2$


$latex \left\langle \phi_n|\phi_m\right\rangle=\delta_{nm}&s=2$


$latex \sum_{n=1}^{\infty} \left|\phi_n\right\rangle\left\langle\phi_n\right|=\hat I&s=2$

With this we could write any arbitrary state of the system as

$latex \left|\psi\right\rangle = \sum_{n=1}^{\infty} \left|\phi_n\right\rangle\left\langle\phi_n|\psi\right\rangle&s=2$

Here $latex \left\langle\phi_n|\psi\right\rangle$ are the expansion coefficients (or probability amplitudes) whose modulus square  $latex |\left\langle\phi_n|\psi\right\rangle|^2$ is the probability that upon measurement the system will return energy $latex E_n$ associated with the eigenvector $latex \left|\phi_n\right\rangle$.

Lets now ask the question

Where is the particle in the box?

To answer this question we need to look first at Position Operator








4 responses to “Particle in a box 2”

  1. […] After this short summary you can look again at A Particle in a Box- 1or to a brief summary in Particle in a box 2. […]

  2. Abubakar Avatar

    These are abysmally amazing articles written in really pellucid and explicit way. Above all they are so easy to understand. They can be made better by adding links for additional reading. Overall they are flabbergasting.

  3. Shahzaib Rahat Avatar
    Shahzaib Rahat

    Can we say that a ket if represented in term of eignvectors(which we know r base vecters) is a superpostion state of a partical .Becz that ket is being represented as liner combination of those eignvectors.

    1. Faheel Hashmi Avatar

      Yes, the system ket will either be eigenket of some observable or the superposition of the eigenkets of that observable

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