Did Schrodinger's cat explore Tolkien's garden?

In 1935 Schrodinger wrote his famous paper (with the cat) introducing the term entanglement, in response to the Einstein-Podolsky-Rosen paper published earlier that year.

When Schrodinger wrote the paper he was living in a house on Northmoor Road, Oxford. This was the same house where Schrodinger learned he had been awarded the Nobel Prize.

I recently learned some fascinating historical trivia.
Schrodinger was a neighbour of J.R.R. Tolkien, who during that time was finishing up work on The Hobbit.

It would be nice to see this landmark honoured, such as the one on Tolkien's house. However, it seems Schrodinger's house does not meet the criteria of Oxfordshire Blue Plaques Board, because he lived there for three years, less than the required minimum of five years.

Another option would be a plaque of the Institute of Physics, such as this one.