Electrochemical half cell without redox couple
Nernst's equation

The Nernst Equation can be derived from the Gibbs energy $\Delta G = nFE $. The free energy for a cell reaction:

$$\Delta G = \Delta G^\circ - RT \ln Q$$ 

can be written as:

$$E = E^\circ - \frac {RT}{nF} \ln Q$$ 

for reaction 

$$\ce{O + $n$e -&gt; R}$$ 

$$E = E^\circ -  \frac{RT}{nF} \ln\frac{a_\mathrm R}{a_\mathrm O}$$

where $a_i$ is activity of species $i$. 

Activity
In a solution, the activity of $i$ is defined: $a_i=\gamma_i \frac {C_i}{C^0}$ where $C_i$ is the concentration of solute, $C^\circ$ is standard concentration ($1\ \mathrm M$), and $\gamma_i$ is unitless activity coefficient.

The equation can be simplified in:

$$E = E^{\circ'} -  \frac{RT}{nF} \ln\frac{[\ce{R}]}{[\ce{O}]}$$

But for the reaction

$$\ce{Cu^2+ + 2e- -&gt; Cu}$$

the Nernst's equation will be:

$$
E = E^{\circ'} -  \frac{RT}{nF} \ln\frac{[\ce{R}]=1}{[\ce{O}]}
$$

because activity of solid (deposited copper) is 1.

If you try to calculate the potential of $0.01\ \mathrm M$ solution you will obtain the difference between standard concentration and the potential at $0.01\ \mathrm M$. 

$$\begin{align}
E &amp;= E^{\circ'} -  \frac{0.02559\ \mathrm V}{2} \ln\frac{1}{0.63}\\[6pt]
&amp;= 0.34\ \mathrm V -  0.0059\ \mathrm V
\end{align}$$

The computed potential ($0.0059\ \mathrm V$) is lower than the standard potential and they are probably neglecting it.