Consider the following state vectors: .
Calculate (i) the norm of and (ii) the inner product
.
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Consider the following state vectors: .
Calculate (i) the norm of and (ii) the inner product
.
i) Normalize the wave function:
ii) Calculate the expectation value of x for a particle in this state.
A quantum mechanical particle in one dimension has the wave function:
Use the Schrödinger equation to determine the corresponding potential V(x).
and
are the orthonormal basis states of a two-dimensional Hilbert space. A Hermitian operator
in this basis is given by the spectral representation:
. For a normalized state given by
Show that in the terms of the and
basis vectors defined by
;
, we can write:
i) Write down the angular momentum states and calculate the matrix elements of
and
for
.
ii) For the angular momentum state show that
and
.
Show that for any stationary state of a symmetric potential well: .