What "nutrients" does a canna need?  

I am astounded that you are recommending planting anything that
requires so much water in Tucson/Phoenix. Your diminishing water
resources make this an irresponsible choice, not to mention the fact
that the Arizona water is so full of sodium that plants either fail
to thrive or actually die due to excess salt, especially in
containers, unless they evolved along with the soil/water situation.
As my daughter is a U. of A. graduate student working on her PhD in
soil science and hydrology, I can provide you with a lot of research
to back this up. I would recommend that you maybe talk to people
like Scott Calhoun to find something more suitable than Canna for
containers. 

Can you dig them up once they've grown so that you can share them
now?

I’ve been out of town away from computer access so apologize for the
delayed response to comments.

Cynthia, cannas do well with a fertilizer for flowering plants that
has a higher middle number, such as 5-10-5 or 15-30-15. Here’s some
basic info on fertilizer and nutrients that plants require.  The 3
numbers on a fertilizer bag refer to the percentage of N (nitrogen),
P (phosphorus), and K (potassium) in the bag. There are different
formulations for different purposes. In general terms, nitrogen
produces lush green growth, phosphorus helps strengthen stems and
produce flowers, and potassium keeps the root system healthy. Rock
phosphate is an organic source of phosphorus.

Renee, any bulb-type plant’s foliage is providing energy to the bulb
for the next growing season, so the best time to dig and divide is
after the foliage has died back completely but before you forget
where they are! For cannas, that’s late fall.

Hilary, I also work at the University of Arizona Cooperative
Extension Horticulture Department in Maricopa County, so am well
versed in our soil and water conditions. I’ve explained such
concepts to the gardening public in dozens of articles as well as
books such as Desert Gardening for Beginners and Earth-Friendly
Desert Gardening. Also, for almost two decades, I’ve profiled
gardeners with various backgrounds and abilities. Probably the most
interesting thing I’ve discovered in these interviews is how many of
these now die-hard desert gardeners started out not particularly
enthused about desert plants or xeriscapes, but through their
gardening experiences, came to appreciate the beauty and unique
characteristics of native plants and the value of desert-friendly
landscapes. A recent profile provides a good example: she started
out as a rose gardener, but now she can’t get enough of the form and
texture provided by cacti and other succulents and has created a
special planting area to showcase unique examples. This spring she
changed her front yard to xeriscape. Although in some folks’ version
of a “perfect” gardening world, there would be only native plants,
in reality, that’s a difficult vision to enforce, especially with a
transient population. From years of public interaction, we’ve found
it works much better to provide viable options that may appeal to
different gardeners in different ways, and by giving them
appropriate information to achieve success in our arid climate, they
will continue further down the gardening path to desert-adapted
landscapes. Canna, as described in this article, works for that
purpose. Thanks for sharing your point of view.