Matter waves as standing waves

[GAGS]

Hi all,can anyone tell me the meaning of lines that i had read from a book:
"The electron is situated within a distance of 10 to the power -8 to 10 to the power -10 m. from the nucleus and is always confined only within this distace. The matter waves associated with electron is defined in terms of standing waves or stationary wave,which have varying amplitude at different points in the region and practically zero outside the range"
Now i have two questions
1.)Why matter waves associated with electron is regarded as standing wave?
2.)The definition of standing wave says that amplitude is constant within a confined range,but here we are saying that amplitude is varying at different points within the range.
WHATS THAT DILEMMA?
please help me.
thanks

 

[DrClaude]

1.)Why matter waves associated with electron is regarded as standing wave?

Because it is a solution to the time-independent Schrödinger equation, which is a wave equation.

2.)The definition of standing wave says that amplitude is constant within a confined range,but here we are saying that amplitude is varying at different points within the range.

A classical standing wave also has an amplitude that varies with position.